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Journal articles on the topic 'Hyperchaotic system'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 June 2024

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1

MA, CHAO, and XINGYUAN WANG. "BRIDGE BETWEEN THE HYPERCHAOTIC LORENZ SYSTEM AND THE HYPERCHAOTIC CHEN SYSTEM." International Journal of Modern Physics B 25, no. 05 (February 20, 2011): 711–21. http://dx.doi.org/10.1142/s0217979211057967.

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This paper presents a novel unified hyperchaotic system that contains the hyperchaotic Lorenz system and the hyperchaotic Chen system as two dual systems at the two extremes of its parameter spectrum. The new system is hyperchaotic over almost the whole range of the system parameter and continuously transfers from the hyperchaotic Lorenz system to the hyperchaotic Chen system. The new findings are not only demonstrated by computer simulations but also verified with bifurcation analysis, Lyapunov exponents and Lyapunov dimension.

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2

Sahin, Muhammet Emin, Hasan Guler, and Serdar Ethem Hamamci. "Design and Realization of a Hyperchaotic Memristive System for Communication System on FPGA." Traitement du Signal 37, no. 6 (December 31, 2020): 939–53. http://dx.doi.org/10.18280/ts.370607.

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In this study, a memristor based hyperchaotic circuit is presented and implemented for communication systems on FPGA platform. Four dimensional hyperchaotic system, which contains active flux controlled memristor is designed by using a smooth continuous nonlinearity. Dynamical characteristics of designed hyperchaotic circuit are examined such as equilibrium points, chaotic attractors, Lyapunov exponents and bifurcation diagram. Furthermore, an electronic circuit model of hyperchaotic system has been modeled and results are submitted. Chaotic circuits are used in communication systems especially in secure communication due to their sensitive dependence on the initial conditions, not periodic, and having a spread spectrum. By using nonlinearity of memristor, the signals obtained from memristor based hyperchaotic system have been realized to analog and digital communication schemes on FPGA platform, which is suitable for re-programmable and reconfigurable systems. The success of memristor based hyperchaotic circuit with FPGA based communication is demonstrated by both simulation and experimental results.

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3

Vaidyanathan, Sundarapandian. "Hyperchaos, adaptive control and synchronization of a novel 4-D hyperchaotic system with two quadratic nonlinearities." Archives of Control Sciences 26, no. 4 (December 1, 2016): 471–95. http://dx.doi.org/10.1515/acsc-2016-0026.

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AbstractThis research work announces an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. We describe the qualitative properties of the novel 4-D hyperchaotic system and illustrate their phase portraits. We show that the novel 4-D hyperchaotic system has two unstable equilibrium points. The novel 4-D hyperchaotic system has the Lyapunov exponents L1= 3.1575, L2= 0.3035, L3= 0 and L4= −33.4180. The Kaplan-Yorke dimension of this novel hyperchaotic system is found as DKY= 3.1026. Since the sum of the Lyapunov exponents of the novel hyperchaotic system is negative, we deduce that the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to stabilize the novel 4-D hyperchaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 4-D hyperchaotic systems with unknown system parameters. The adaptive control results are established using Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results derived in this research work.

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4

Xiong, Li, Zhenlai Liu, and Xinguo Zhang. "Dynamical Analysis, Synchronization, Circuit Design, and Secure Communication of a Novel Hyperchaotic System." Complexity 2017 (2017): 1–23. http://dx.doi.org/10.1155/2017/4962739.

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This paper is devoted to introduce a novel fourth-order hyperchaotic system. The hyperchaotic system is constructed by adding a linear feedback control level based on a modified Lorenz-like chaotic circuit with reduced number of amplifiers. The local dynamical entities, such as the basic dynamical behavior, the divergence, the eigenvalue, and the Lyapunov exponents of the new hyperchaotic system, are all investigated analytically and numerically. Then, an active control method is derived to achieve global chaotic synchronization of the novel hyperchaotic system through making the synchronization error system asymptotically stable at the origin based on Lyapunov stability theory. Next, the proposed novel hyperchaotic system is applied to construct another new hyperchaotic system with circuit deformation and design a new hyperchaotic secure communication circuit. Furthermore, the implementation of two novel electronic circuits of the proposed hyperchaotic systems is presented, examined, and realized using physical components. A good qualitative agreement is shown between the simulations and the experimental results around 500 kHz and below 1 MHz.

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5

Chai, Yi, Liping Chen, and Ranchao Wu. "Inverse Projective Synchronization between Two Different Hyperchaotic Systems with Fractional Order." Journal of Applied Mathematics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/762807.

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This paper mainly investigates a novel inverse projective synchronization between two different fractional-order hyperchaotic systems, that is, the fractional-order hyperchaotic Lorenz system and the fractional-order hyperchaotic Chen system. By using the stability theory of fractional-order differential equations and Lyapunov equations for fractional-order systems, two kinds of suitable controllers for achieving inverse projective synchronization are designed, in which the generalized synchronization, antisynchronization, and projective synchronization of fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system are also successfully achieved, respectively. Finally, simulations are presented to demonstrate the validity and feasibility of the proposed method.

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6

Wang Xing-Yuan and Wang Ming-Jun. "Hyperchaotic Lorenz system." Acta Physica Sinica 56, no. 9 (2007): 5136. http://dx.doi.org/10.7498/aps.56.5136.

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7

Wu, Yan-Ping, and Guo-Dong Wang. "Synchronization between Fractional-Order and Integer-Order Hyperchaotic Systems via Sliding Mode Controller." Journal of Applied Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/151025.

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The synchronization between fractional-order hyperchaotic systems and integer-order hyperchaotic systems via sliding mode controller is investigated. By designing an active sliding mode controller and choosing proper control parameters, the drive and response systems are synchronized. Synchronization between the fractional-order Chen chaotic system and the integer-order Chen chaotic system and between integer-order hyperchaotic Chen system and fractional-order hyperchaotic Rössler system is used to illustrate the effectiveness of the proposed synchronization approach. Numerical simulations coincide with the theoretical analysis.

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8

Vaidyanathan, Sundarapandian, Christos Volos, and Viet-Thanh Pham. "Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation." Archives of Control Sciences 24, no. 4 (December 1, 2014): 409–46. http://dx.doi.org/10.2478/acsc-2014-0023.

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Abstract In this research work, a twelve-term novel 5-D hyperchaotic Lorenz system with three quadratic nonlinearities has been derived by adding a feedback control to a ten-term 4-D hyperchaotic Lorenz system (Jia, 2007) with three quadratic nonlinearities. The 4-D hyperchaotic Lorenz system (Jia, 2007) has the Lyapunov exponents L1 = 0.3684,L2 = 0.2174,L3 = 0 and L4 =−12.9513, and the Kaplan-Yorke dimension of this 4-D system is found as DKY =3.0452. The 5-D novel hyperchaotic Lorenz system proposed in this work has the Lyapunov exponents L1 = 0.4195,L2 = 0.2430,L3 = 0.0145,L4 = 0 and L5 = −13.0405, and the Kaplan-Yorke dimension of this 5-D system is found as DKY =4.0159. Thus, the novel 5-D hyperchaotic Lorenz system has a maximal Lyapunov exponent (MLE), which is greater than the maximal Lyapunov exponent (MLE) of the 4-D hyperchaotic Lorenz system. The 5-D novel hyperchaotic Lorenz system has a unique equilibrium point at the origin, which is a saddle-point and hence unstable. Next, an adaptive controller is designed to stabilize the novel 5-D hyperchaotic Lorenz system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 5-D hyperchaotic Lorenz systems with unknown system parameters. Finally, an electronic circuit realization of the novel 5-D hyperchaotic Lorenz system using SPICE is described in detail to confirm the feasibility of the theoretical model.

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9

Chai, Xiuli, Zhihua Gan, and Chunxiao Shi. "Adaptive Modified Function Projective Lag Synchronization of Uncertain Hyperchaotic Dynamical Systems with the Same or Different Dimension and Structure." Mathematical Problems in Engineering 2013 (2013): 1–15. http://dx.doi.org/10.1155/2013/282064.

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Modified function projective lag synchronization (MFPLS) of uncertain hyperchaotic dynamical systems with the same or different dimensions and structures is studied. Based on Lyapunov stability theory, a general theorem for controller designing, parameter update rule designing, and control gain strength adapt law designing is introduced by using adaptive control method. Furthermore, the scheme is applied to four typical examples: MFPLS between two five-dimensional hyperchaotic systems with the same structures, MFPLS between two four-dimensional hyperchaotic systems with different structures, MFPLS between a four-dimensional hyperchaotic system and a three-dimensional chaotic system and MFPLS between a novel three-dimensional chaotic system, and a five-dimensional hyperchaotic system. And the system parameters are all uncertain. Corresponding numerical simulations are performed to verify and illustrate the analytical results.

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10

BAO, BOCHENG, JIANPING XU, ZHONG LIU, and ZHENGHUA MA. "HYPERCHAOS FROM AN AUGMENTED LÜ SYSTEM." International Journal of Bifurcation and Chaos 20, no. 11 (November 2010): 3689–98. http://dx.doi.org/10.1142/s0218127410027969.

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This letter introduces a hyperchaotic system from the Lü system [Lü et al., 2004] with a linear state feedback controller. This hyperchaotic system has more complex dynamical behaviors, and can generate 4-scroll hyperchaotic attractor and 2-scroll chaotic attractor under different control parameters. In particular, the system can also exhibit novel coexisting intermittent chaotic orbits. Theoretical analyses and simulation experiments are conducted to investigate the dynamical behaviors of the proposed hyperchaotic system.

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11

Vaidyanathan, Sundarapandian, Aceng Sambas, Mohamad Afendee, Mustafa Mamat, and Mada Sanjaya. "A New Hyperchaotic Hyperjerk System with Three Nonlinear Terms, its Synchronization and Circuit Simulation." International Journal of Engineering & Technology 7, no. 3 (July 25, 2018): 1585. http://dx.doi.org/10.14419/ijet.v7i3.14760.

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In recent decades, hyperjerk systems have been studied well in the literature because of their simple dynamics structure and complex qualitative properties. In this work, we announce a new hyperchaotic hyperjerk system with three nonlinear terms. Dynamical properties of the hyperjerk system are analyzed through equilibrium analysis, dissipativity, phase portraits and Lyapunov chaos exponents. We show that the new hyperchaotic hyperjerk system has a unique saddle-focus equilibrium at the origin. Thus, the new hyperchaotic hyperjerk system has a self-excited strange attractor. Next, global hyperchaos synchronization of a pair of new hyperchaotic hyperjerk systems is successfully achieved via adaptive backstepping control. Also, an electronic circuit of the hyperchaotic hyperjerk system has been designed via MultiSIM to check the feasibility of the theoretical system.

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12

El-Dessoky, M. M., M. T. Yassen, and E. Saleh. "Adaptive Modified Function Projective Synchronization between Two Different Hyperchaotic Dynamical Systems." Mathematical Problems in Engineering 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/810626.

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This work investigates modified function projective synchronization between two different hyperchaotic dynamical systems, namely, hyperchaotic Lorenz system and hyperchaotic Chen system with fully unknown parameters. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived to achieve modified function projective synchronized between two diffierent hyperchaotic dynamical systems. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.

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13

YANG, QIGUI, and CHUNTAO CHEN. "A 5D HYPERCHAOTIC SYSTEM WITH THREE POSITIVE LYAPUNOV EXPONENTS COINED." International Journal of Bifurcation and Chaos 23, no. 06 (June 2013): 1350109. http://dx.doi.org/10.1142/s0218127413501095.

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This paper reports the finding of a five-dimensional (5D) new hyperchaotic system with three positive Lyapunov exponents, which is obtained by adding a nonlinear controller to the first equation of a 4D hyperchaotic system. The algebraical form of the hyperchaotic system is very similar to the 5D controlled Lorenz-like systems but they are different and, in fact, nonequivalent in topological structures. Of particular interest is the fact that the hyperchaotic system has a hyperchaotic attractor with three positive Lyapunov exponents under unique equilibrium or three equilibria. To further analyze the new system, the corresponding hyperchaotic and chaotic attractor are firstly numerically verified through investigating phase trajectories, Lyapunov exponents, bifurcation, analysis of power spectrum and Poincaré projections. Moreover, some complex dynamical behaviors such as the stability of hyperbolic or nonhyperbolic equilibrium and two complete mathematical characterizations for 5D Hopf bifurcation are rigorously derived and studied.

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14

ZHANG, HONGBIN, CHUNGUANG LI, GUANRONG CHEN, and XING GAO. "HYPERCHAOS IN THE FRACTIONAL-ORDER NONAUTONOMOUS CHEN'S SYSTEM AND ITS SYNCHRONIZATION." International Journal of Modern Physics C 16, no. 05 (May 2005): 815–26. http://dx.doi.org/10.1142/s0129183105007510.

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Recently, a new hyperchaos generator, obtained by controlling a three-dimensional autonomous chaotic system — Chen's system — with a periodic driving signal, has been found. In this letter, we formulate and study the hyperchaotic behaviors in the corresponding fractional-order hyperchaotic Chen's system. Through numerical simulations, we found that hyperchaos exists in the fractional-order hyperchaotic Chen's system with order less than 4. The lowest order we found to have hyperchaos in this system is 3.4. Finally, we study the synchronization problem of two fractional-order hyperchaotic Chen's systems.

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15

WANG, XING-YUAN, YU-HONG YANG, and MING-KU FENG. "SYNCHRONIZATION BETWEEN TWO DIFFERENT HYPERCHAOTIC SYSTEMS WITH UNCERTAIN PARAMETERS." International Journal of Modern Physics B 27, no. 13 (May 15, 2013): 1350044. http://dx.doi.org/10.1142/s0217979213500446.

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This paper studies the problem of chaos synchronization between two different hyperchaotic systems with uncertain parameters. Based on the Lyapunov stability theory, we obtain the sufficient condition of synchronization between two different hyperchaotic systems with uncertain parameters. A new adaptive controller with parameter update laws is designed to synchronize these chaotic systems. We proved it in theory with an uncertain hyperchaotic Lorenz system and an uncertain hyperchaotic Rössler system. Numerical results verified the validation of the proposed scheme.

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16

WANG, XINGYUAN, DAHAI NIU, and MINGJUN WANG. "ACTIVE TRACKING CONTROL OF THE HYPERCHAOTIC LORENZ SYSTEM." Modern Physics Letters B 22, no. 19 (July 30, 2008): 1859–65. http://dx.doi.org/10.1142/s0217984908016534.

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A nonlinear active tracking controller for the four-dimensional hyperchaotic Lorenz system is designed in the paper. The controller enables this hyperchaotic system to track all kinds of reference signals, such as the sinusoidal signal. The self-synchronization of the hyperchaotic Lorenz system and the different-structure synchronization with other chaotic systems can also be realized. Numerical simulation results show the effectiveness of the controller.

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17

Rajagopal, Karthikeyan, Laarem Guessas, Sundarapandian Vaidyanathan, Anitha Karthikeyan, and Ashokkumar Srinivasan. "Dynamical Analysis and FPGA Implementation of a Novel Hyperchaotic System and Its Synchronization Using Adaptive Sliding Mode Control and Genetically Optimized PID Control." Mathematical Problems in Engineering 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/7307452.

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We announce a new 4D hyperchaotic system with four parameters. The dynamic properties of the proposed hyperchaotic system are studied in detail; the Lyapunov exponents, Kaplan-Yorke dimension, bifurcation, and bicoherence contours of the novel hyperchaotic system are derived. Furthermore, control algorithms are designed for the complete synchronization of the identical hyperchaotic systems with unknown parameters using sliding mode controllers and genetically optimized PID controllers. The stabilities of the controllers and parameter update laws are proved using Lyapunov stability theory. Use of the optimized PID controllers ensures less time of convergence and fast synchronization speed. Finally the proposed novel hyperchaotic system is realized in FPGA.

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18

Yi, Lingzhi, Weihong Xiao, Wenxin Yu, and Binren Wang. "Dynamical analysis, circuit implementation and deep belief network control of new six-dimensional hyperchaotic system." Journal of Algorithms & Computational Technology 12, no. 4 (July 25, 2018): 361–75. http://dx.doi.org/10.1177/1748301818788649.

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In this paper, a new six-dimensional hyperchaotic system is proposed and some basic dynamical properties including bifurcation diagrams, Lyapunov exponents and phase portraits are investigated. Furthermore, the electronic circuit of this novel hyperchaotic system is simulated on the Multisim platform, and the simulation results are agreed well with the numerical simulation of the same hyperchaotic system on the Matlab platform. Finally, a control method based on Deep Belief Network is proposed to track and control the proposed hyperchaotic system. In this method, the function of the hyperchaotic system is studied by Deep Belief Network and a high precision fitting function is obtained. Then a controller which is composed of the fitting function and the tracking reference signal is designed to achieve the tracking control of hyperchaotic systems. Simulation results verify the effectiveness and feasibility of this method.

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19

Li, Xiang, Zhijun Li, and Zihao Wen. "One-to-four-wing hyperchaotic fractional-order system and its circuit realization." Circuit World 46, no. 2 (January 10, 2020): 107–15. http://dx.doi.org/10.1108/cw-03-2019-0026.

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Purpose This paper aims to introduce a novel 4D hyperchaotic fractional-order system which can produce one-to-four-wing hyperchaotic attractors. In the study of chaotic systems with variable-wing attractors, although some chaotic systems can generate one-to-four-wing attractors, none of them are hyperchaotic attractors, which is incomplete for the dynamic characteristics of chaotic systems. Design/methodology/approach A novel 4D fractional-order hyperchaotic system is proposed based on the classical three-dimensional Lü system. The complex and abundant dynamic behaviors of the fractional-order system are analyzed by phase diagrams, bifurcation diagrams and the corresponding Lyapunov exponents. In addition, SE and C0 algorithms are used to analyze the complexity of the fractional-order system. Then, the influence of order q on the system is also investigated. Finally, the circuit is implemented using physical components. Findings The most particular interest is that the system can generate one-to-four-wing hyperchaotic attractors with only one parameter variation. Then, the hardware circuit experimental results tally with the numerical simulations, which proves the validity and feasibility of the fractional-order hyperchaotic system. Besides, under different initial conditions, coexisting attractors can be obtained by changing the parameter d or the order q. Then, the complexity analysis of the system shows that the fractional-order chaotic system has higher complexity than the corresponding integer-order chaotic system. Originality/value The circuit structure of the fractional-order hyperchaotic system is simple and easy to implement, and one-to-four-wing hyperchaotic attractors can be observed in the circuit. To the best of the knowledge, this unique phenomenon has not been reported in any literature. It is of great reference value to analysis and circuit realization of fractional-order chaotic systems.

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20

Jiao, Xiaodong, Enzeng Dong, and Zenghui Wang. "Dynamic Analysis and FPGA Implementation of a Kolmogorov-Like Hyperchaotic System." International Journal of Bifurcation and Chaos 31, no. 04 (March 30, 2021): 2150052. http://dx.doi.org/10.1142/s0218127421500528.

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Chaotic systems have high potential for engineering applications due to their extremely complex dynamics. In the paper, a five-dimensional (5D) Kolmogorov-like hyperchaotic system is proposed. First, the hyperchaotic property is uncovered, and numerical analysis shows that the system displays the coexistence of different kinds of attractors. This system presents a generalized form of fluid and forced-dissipative dynamic systems. The vector field of the hyperchaotic system is decomposed to inertial, internal, dissipative and external torques, respectively, and the energies are analyzed in detail. Then, the bound of the 5D dissipative hyperchaos is estimated with a constructed spherical function. Finally, the system passes the NIST tests and an FPGA platform is used to realize the hyperchaotic system.

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21

Liang, Feng, Lu Lu, Zhengfeng Li, Fangfang Zhang, and Shuaihu Zhang. "Tracking Control of a Hyperchaotic Complex System and Its Fractional-Order Generalization." Processes 10, no. 7 (June 22, 2022): 1244. http://dx.doi.org/10.3390/pr10071244.

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Hyperchaotic complex behaviors often occur in nature. Some chaotic behaviors are harmful, while others are beneficial. As for harmful behaviors, we hope to transform them into expected behaviors. For beneficial behaviors, we want to enhance their chaotic characteristics. Aiming at the harmful hyperchaotic complex system, a tracking controller was designed to produce the hyperchaotic complex system track common expectation system. We selected sine function, constant, and complex Lorenz chaotic system as target systems and verified the effectiveness by mathematical proof and simulation experiments. Aiming at the beneficial hyperchaotic complex phenomenon, this paper extended the hyperchaotic complex system to the fractional order because the fractional order has more complex dynamic characteristics. The influences order change and parameter change on the evolution process of the system were analyzed and observed by MATLAB simulation.

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22

Zhou, Ping, and Rui Ding. "A Novel Hyperchaotic System and its Circuit Implementation." Key Engineering Materials 467-469 (February 2011): 321–24. http://dx.doi.org/10.4028/www.scientific.net/kem.467-469.321.

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A hyperchaotic system with only one nonlinear term is presented. The Lyapunov exponents, Lyapunov fractal dimensions, and phase diagram of this hyperchaotic system are obtained. Furthermore, one electronic oscillator circuit design of this hyperchaotic system is described using the Electronics Work Bench (EWB).

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23

Ozpolat, Erman, and Arif Gulten. "Synchronization and Application of a Novel Hyperchaotic System Based on Adaptive Observers." Applied Sciences 14, no. 3 (February 5, 2024): 1311. http://dx.doi.org/10.3390/app14031311.

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This paper explores the synchronization and implementation of a novel hyperchaotic system using an adaptive observer. Hyperchaotic systems, known for possessing a greater number of positive Lyapunov exponents compared to chaotic systems, present unique challenges and opportunities in control and synchronization. In this study, we introduce a novel hyperchaotic system, thoroughly examining its dynamic properties and conducting a comprehensive phase space analysis. The proposed hyperchaotic system undergoes validation through circuit simulation to confirm its behavior. Introducing an adaptive observer synchronization technique, we successfully synchronize the dynamics of the novel hyperchaotic system with an identical counterpart. Importantly, we extend the application of this synchronization method to the domain of secure communication, showcasing its practical usage. Simulation outcomes validate the effectiveness of our methodology, demonstrating favorable results in the realm of adaptive observer-based synchronization. This research contributes significantly to the understanding and application of hyperchaotic systems, offering insights into both the theoretical aspects and practical implementation. Our findings suggest potential advancements in the field of chaotic systems, particularly in their applications within secure communication systems. By presenting motivations, methods, results, conclusions and the significance of our work in a more appealing manner, we aim to engage readers and highlight the innovative contributions of this study.

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Wei, Zhouchao. "Synchronization of Coupled Nonidentical Fractional-Order Hyperchaotic Systems." Discrete Dynamics in Nature and Society 2011 (2011): 1–9. http://dx.doi.org/10.1155/2011/430724.

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Synchronization of coupled nonidentical fractional-order hyperchaotic systems is addressed by the active sliding mode method. By designing an active sliding mode controller and choosing proper control parameters, the master and slave systems are synchronized. Furthermore, synchronizing fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system is performed to show the effectiveness of the proposed controller.

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NIAN, FUZHONG, and XINGYUAN WANG. "PROJECTIVE SYNCHRONIZATION OF TWO DIFFERENT DIMENSIONAL NONLINEAR SYSTEMS." International Journal of Modern Physics B 27, no. 21 (July 30, 2013): 1350113. http://dx.doi.org/10.1142/s0217979213501130.

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Projective synchronization between two nonlinear systems with different dimension was investigated. The controllers were designed when the dimension of drive system greater than the one of response system. The opposite situation also was discussed. In addition, we found an approach to control the chaotic (hyperchaotic) system to exhibit the behaviors of hyperchaotic (chaotic) system. The numerical simulations were implemented on different chaotic (hyperchaotic) systems, and the results indicate that our methods are effective.

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Zheng, Jiming, and Bingfang Du. "Projective Synchronization of Hyperchaotic Financial Systems." Discrete Dynamics in Nature and Society 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/782630.

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Based on a special matrix structure, the projective synchronization control laws of the hyperchaotic financial systems are proposed in this paper. Put a hyperchaotic financial system as the drive system, via transformation of the system state variables, construct its response system, and then design the controller based on the special matrix structure. The given scheme is applied to achieve projective synchronization of the different hyperchaotic financial systems. Numerical experiments demonstrate the effectiveness of the method.

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Plata, Corina, Pablo J. Prieto, Ramon Ramirez-Villalobos, and Luis N. Coria. "Chaos Synchronization for Hyperchaotic Lorenz-Type System via Fuzzy-Based Sliding-Mode Observer." Mathematical and Computational Applications 25, no. 1 (March 14, 2020): 16. http://dx.doi.org/10.3390/mca25010016.

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Hyperchaotic systems have applications in multiple areas of science and engineering. The study and development of these type of systems helps to solve diverse problems related to encryption and decryption of information. In order to solve the chaos synchronization problem for a hyperchaotic Lorenz-type system, we propose an observer based synchronization under a master-slave configuration. The proposed methodology consists of designing a sliding-mode observer (SMO) for the hyperchaotic system. In contrast, this type of methodology exhibits high-frequency oscillations, commonly known as chattering. To solve this problem, a fuzzy-based SMO system was designed. Numerical simulations illustrate the effectiveness of the synchronization between the hyperchaotic system obtained and the proposed observer.

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El-Dessoky, M. M., and E. Saleh. "Generalized Projective Synchronization for Different Hyperchaotic Dynamical Systems." Discrete Dynamics in Nature and Society 2011 (2011): 1–19. http://dx.doi.org/10.1155/2011/437156.

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Projective synchronization and generalized projective synchronization have recently been observed in the coupled hyperchaotic systems. In this paper a generalized projective synchronization technique is applied in the hyperchaotic Lorenz system and the hyperchaotic Lü. The sufficient conditions for achieving projective synchronization of two different hyperchaotic systems are derived. Numerical simulations are used to verify the effectiveness of the proposed synchronization techniques.

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Yang, Qigui, Lingbing Yang, and Bin Ou. "Hidden Hyperchaotic Attractors in a New 5D System Based on Chaotic System with Two Stable Node-Foci." International Journal of Bifurcation and Chaos 29, no. 07 (June 30, 2019): 1950092. http://dx.doi.org/10.1142/s0218127419500925.

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This paper reports some hidden hyperchaotic attractors and complex dynamics in a new five-dimensional (5D) system with only two nonlinear terms. The system is generated by adding two linear controllers to an unusual 3D autonomous quadratic chaotic system with two stable node-foci. In particular, the hyperchaotic system without equilibrium or with only one stable equilibrium can generate two kinds of hidden hyperchaotic attractors with three positive Lyapunov exponents. Numerical methods not only verify the existence of such attractors and hyperchaotic attractors, but also show the dynamical evolution of this system. The 5D system has self-excited attractors and two types of hidden attractors with the change of its parameter. The parameter switching algorithm is further utilized to numerically approximate the attractor. Specifically, the hidden hyperchaotic attractor can be approximated by switching between two self-excited chaotic attractors. Finally, the circuit realization results are consistent with the numerical results.

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RECH, PAULO C., and HOLOKX A. ALBUQUERQUE. "A HYPERCHAOTIC CHUA SYSTEM." International Journal of Bifurcation and Chaos 19, no. 11 (November 2009): 3823–28. http://dx.doi.org/10.1142/s0218127409025146.

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In this paper, we report a new four-dimensional autonomous hyperchaotic system, constructed from a Chua system where the piecewise-linear function usually taken to describe the nonlinearity of the Chua diode has been replaced by a cubic polynomial. Analytical and numerical procedures are conducted to study the dynamical behavior of the proposed new hyperchaotic system.

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Tao, Si Yan, Da Lin, and Xiao Hui Zeng. "Generalized Projective Synchronization of Diverse Structures Hyperchaotic Systems with Unknown Parameters." Applied Mechanics and Materials 568-570 (June 2014): 1095–99. http://dx.doi.org/10.4028/www.scientific.net/amm.568-570.1095.

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In this paper, the generalized projective synchronization for a general class of hyperchaotic systems is investigated. A systematic, powerful and concrete scheme is developed to investigate the generalized projective synchronization between the drive system and response system based on the feedback control approach. The hyperchaotic Chen system and hyperchaotic Lorenz system are chosen to illustrate the proposed scheme. Numerical simulations are provided to show the effectiveness of the proposed schemes.

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LIU, ZHI-YU, CHIA-JU LIU, MING-CHUNG HO, YAO-CHEN HUNG, TZU-FANG HSU, and I.-MIN JIANG. "SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC AND CHAOTIC SYSTEMS BY ADAPTIVE CONTROL." International Journal of Bifurcation and Chaos 18, no. 12 (December 2008): 3731–36. http://dx.doi.org/10.1142/s0218127408022688.

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This paper presents the synchronization between uncertain hyperchaotic and chaotic systems. Based on Lyapunov stability theory, an adaptive controller is derived to achieve synchronization of hyperchaotic and chaotic systems, including the case of unknown parameters in these two systems. The T.N.Č. hyperchaotic oscillator is used as the master system, and the Rössler system is used as the slave system. Numerical simulations verify these results. Additionally, the effect of noise is investigated by measuring the mean squared error (MSE) of two systems.

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Zhang, Fuchen, Rui Chen, and Xiusu Chen. "Analysis of a Generalized Lorenz–Stenflo Equation." Complexity 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/7520590.

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Although the globally attractive sets of a hyperchaotic system have important applications in the fields of engineering, science, and technology, it is often a difficult task for the researchers to obtain the globally attractive set of the hyperchaotic systems due to the complexity of the hyperchaotic systems. Therefore, we will study the globally attractive set of a generalized hyperchaotic Lorenz–Stenflo system describing the evolution of finite amplitude acoustic gravity waves in a rotating atmosphere in this paper. Based on Lyapunov-like functional approach combining some simple inequalities, we derive the globally attractive set of this system with its parameters. The effectiveness of the proposed methods is illustrated via numerical examples.

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Xu, Chang Jin, and Pei Luan Li. "Chaos Control for a 4D Hyperchaotic System." Applied Mechanics and Materials 418 (September 2013): 84–87. http://dx.doi.org/10.4028/www.scientific.net/amm.418.84.

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In this paper, a four-dimensional (4D) autonomous hyperchaotic system is dealt with. The stability criteria of equilibria of the controlled hyperchaotic chaotic system are established. Using the dislocated feedback control, enhancing feedback control, and nonlinear function feedback control methods, the chaos of the 4D hyperchaotic system can be suppressed to unstable equilibrium. Some numerical simulations revealing the effectiveness of our control strategies are given..

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WANG, XING-YUAN, SI-HUI JIANG, and CHAO LUO. "ADAPTIVE SYNCHRONIZATION OF A NOVEL HYPERCHAOTIC SYSTEM WITH FULLY UNKNOWN PARAMETERS." International Journal of Modern Physics B 27, no. 32 (December 2013): 1350197. http://dx.doi.org/10.1142/s021797921350197x.

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In this paper, a chaotic synchronization scheme is proposed to achieve adaptive synchronization between a novel hyperchaotic system and the hyperchaotic Chen system with fully unknown parameters. Based on the Lyapunov stability theory, an adaptive controller and parameter updating law are presented to synchronize the above two hyperchaotic systems. The corresponding theoretical proof is given and numerical simulations are presented to verify the effectiveness of the proposed scheme.

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Yang, Jiaopeng, and Zhengrong Liu. "A Novel Simple Hyperchaotic System with Two Coexisting Attractors." International Journal of Bifurcation and Chaos 29, no. 14 (December 26, 2019): 1950203. http://dx.doi.org/10.1142/s0218127419502031.

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This article introduces a new hyperchaotic system of four-dimensional autonomous ordinary differential equations, with only cubic cross-product nonlinearities, which can respectively display two hyperchaotic attractors with only nonhyperbolic equilibria line. Several issues such as basic dynamical behaviors, routes to chaos, bifurcations, periodic windows, and the compound structure of the new hyperchaotic and chaotic system are investigated, either theoretically or numerically. Of particular interest is the fact that the two coexisting attractors of the new hyperchaotic system are symmetrical, and this hyperchaotic system can generate plenty of complex dynamics including two coexisting chaotic or periodic attractors. Moreover, some chaotic features of the attractor are justified numerically. Finally, 0-1 test is used to analyze and describe the complex chaotic dynamic behavior of the new system.

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XI, HUILING, SIMIN YU, CHAOXIA ZHANG, and YOULIN SUN. "GENERATION AND IMPLEMENTATION OF HYPERCHAOTIC CHUA SYSTEM VIA STATE FEEDBACK CONTROL." International Journal of Bifurcation and Chaos 22, no. 05 (May 2012): 1250119. http://dx.doi.org/10.1142/s0218127412501192.

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In this paper, a 4D hyperchaotic Chua system both with piecewise-linear nonlinearity and with smooth and piecewise smooth cubic nonlinearity is introduced, based on state feedback control. Dynamical behaviors of this hyperchaotic system are further investigated, including Lyapunov exponents spectrum, bifurcation diagram and solution of state equations. Theoretical analysis and numerical results show that this system can generate multiscroll hyperchaotic attractors. In addition, a circuit is designed for 4D hyperchaotic Chua system such that the double-scroll and 3-scroll hyperchaotic attractors can be physically obtained, demonstrating the effectiveness of the proposed simulation-based techniques.

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WANG, TIANSHU, and XINGYUAN WANG. "GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER HYPERCHAOTIC LORENZ SYSTEM." Modern Physics Letters B 23, no. 17 (July 10, 2009): 2167–78. http://dx.doi.org/10.1142/s021798490902031x.

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In this paper, a type of new fractional order hyperchaotic Lorenz system is proposed. Based on the fractional calculus predictor-corrector algorithm, the fractional order hyperchaotic Lorenz system is investigated numerically, and the simulation results show that the lowest orders for hyperchaos in hyperchaotic Lorenz system is 3.884. According to the stability theory of fractional order system, an improved state-observer is designed, and the response system of generalized synchronization is obtained analytically, whose feasibility is proved theoretically. The synchronization method is adopted to realize the generalized synchronization of 3.884-order hyperchaotic Lorenz system, and the numerical simulation results verify the effectiveness.

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WANG, XINGYUAN, and XIANGJUN WU. "PARAMETER IDENTIFICATION AND ADAPTIVE SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC CHEN SYSTEM." International Journal of Modern Physics B 22, no. 08 (March 30, 2008): 1015–23. http://dx.doi.org/10.1142/s0217979208039034.

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This paper studies the adaptive synchronization and parameter identification of an uncertain hyperchaotic Chen system. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical hyperchaotic Chen systems asymptotically synchronized. With this approach, the synchronization and parameter identification of the hyperchaotic Chen system with five uncertain parameters can be achieved simultaneously. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

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Dong, Enzeng, Mingfeng Yuan, Cong Zhang, Jigang Tong, Zengqiang Chen, and Shengzhi Du. "Topological Horseshoe Analysis, Ultimate Boundary Estimations of a New 4D Hyperchaotic System and Its FPGA Implementation." International Journal of Bifurcation and Chaos 28, no. 07 (June 30, 2018): 1850081. http://dx.doi.org/10.1142/s0218127418500815.

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This paper constructs a new four-dimensional (4D) hyperchaotic system. Firstly, the influence of parameter variation on the dynamic behavior of the system is analyzed in detail using Lyapunov exponents and the bifurcation diagram. Additionally, the topological horseshoe finding algorithm is based on three-dimensional (3D) hyperchaotic mapping. Through searching for the 3D topological horseshoe with two-dimensional stretching on the Poincaré section, the existence of the 4D hyperchaotic system is proved in the mathematical sense. Next, Lyapunov stability theory and optimization method are used to further analyze the ultimate boundary of the proposed 4D hyperchaotic system. Thus, the 3D ellipsoidal boundary of the hyperchaotic system is found. Finally, this paper also takes the hyperchaotic system as an example and presents the experimental results of generated hyperchaotic attractors by FPGA technology. The experimental results show that the phase diagram of hyperchaotic system is consistent for the simulated results. Due to the more complex dynamic behavior, the proposed system is suitable for engineering application, such as in chaotic secure communications.

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Jin-E, Zhang. "Combination-Combination Hyperchaos Synchronization of Complex Memristor Oscillator System." Mathematical Problems in Engineering 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/591089.

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The combination-combination synchronization scheme is based on combination of multidrive systems and combination of multiresponse systems. In this paper, we investigate combination-combination synchronization of hyperchaotic complex memristor oscillator system. Several sufficient conditions are provided to ascertain the combination of two drive hyperchaotic complex memristor oscillator systems to synchronize the combination of two response hyperchaotic complex memristor oscillator systems. These new conditions improve and extend the existing synchronization results for memristive systems. A numerical example is given to show the feasibility of theoretical results.

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Zhou, Xiaofei, Junmei Li, Yulan Wang, and Wei Zhang. "Numerical Simulation of a Class of Hyperchaotic System Using Barycentric Lagrange Interpolation Collocation Method." Complexity 2019 (February 13, 2019): 1–13. http://dx.doi.org/10.1155/2019/1739785.

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Hyperchaotic system, as an important topic, has become an active research subject in nonlinear science. Over the past two decades, hyperchaotic system between nonlinear systems has been extensively studied. Although many kinds of numerical methods of the system have been announced, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, this paper introduces another novel numerical method to solve a class of hyperchaotic system. Barycentric Lagrange interpolation collocation method is given and illustrated with hyperchaotic system (x˙=ax+dz-yz,y˙=xz-by, 0≤t≤T,z˙=cx-z+xy,w˙=cy-w+xz,) as examples. Numerical simulations are used to verify the effectiveness of the present method.

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Liu Ming-Hua and Feng Jiu-Chao. "A new hyperchaotic system." Acta Physica Sinica 58, no. 7 (2009): 4457. http://dx.doi.org/10.7498/aps.58.4457.

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Rezzag, Samia, and Fuchen Zhang. "On the Dynamics of New 4D and 6D Hyperchaotic Systems." Mathematics 10, no. 19 (October 6, 2022): 3668. http://dx.doi.org/10.3390/math10193668.

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One of the most interesting problems is the investigation of the boundaries of chaotic or hyperchaotic systems. In addition to estimating the Lyapunov and Hausdorff dimensions, it can be applied in chaos control and chaos synchronization. In this paper, by means of the analytical optimization, comparison principle, and generalized Lyapunov function theory, we find the ultimate bound set for a new six-dimensional hyperchaotic system and the globally exponentially attractive set for a new four-dimensional Lorenz- type hyperchaotic system. The novelty of this paper is that it not only shows the 4D hyperchaotic system is globally confined but also presents a collection of global trapping regions of this system. Furthermore, it demonstrates that the trajectories of the 4D hyperchaotic system move at an exponential rate from outside the trapping zone to its inside. Finally, some numerical simulations are shown to demonstrate the efficacy of the findings.

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Niu, Yujun, Xuming Sun, Cheng Zhang, and Hongjun Liu. "Anticontrol of a Fractional-Order Chaotic System and Its Application in Color Image Encryption." Mathematical Problems in Engineering 2020 (March 12, 2020): 1–12. http://dx.doi.org/10.1155/2020/6795964.

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This paper investigates the anticontrol of the fractional-order chaotic system. The necessary condition of the anticontrol of the fractional-order chaotic system is proposed, and based on this necessary condition, a 3D fractional-order chaotic system is driven to two new 4D fractional-order hyperchaotic systems, respectively, without changing the parameters and fractional order. Hyperchaotic properties of these new fractional dynamic systems are confirmed by Lyapunov exponents and bifurcation diagrams. Furthermore, a color image encryption algorithm is designed based on these fractional hyperchaotic systems. The effectiveness of their application in image encryption is verified.

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Wu, Aiguo, Shijian Cang, Ruiye Zhang, Zenghui Wang, and Zengqiang Chen. "Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points." Complexity 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/9430637.

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Chaotic dynamics exists in many natural systems, such as weather and climate, and there are many applications in different disciplines. However, there are few research results about chaotic conservative systems especially the smooth hyperchaotic conservative system in both theory and application. This paper proposes a five-dimensional (5D) smooth autonomous hyperchaotic system with nonhyperbolic fixed points. Although the proposed system includes four linear terms and four quadratic terms, the new system shows complicated dynamics which has been proven by the theoretical analysis. Several notable properties related to conservative systems and the existence of perpetual points are investigated for the proposed system. Moreover, its conservative hyperchaotic behavior is illustrated by numerical techniques including phase portraits and Lyapunov exponents.

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Yang, Qigui, Daoyu Zhu, and Lingbing Yang. "A New 7D Hyperchaotic System with Five Positive Lyapunov Exponents Coined." International Journal of Bifurcation and Chaos 28, no. 05 (May 2018): 1850057. http://dx.doi.org/10.1142/s0218127418500578.

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This paper reports the finding of a new seven-dimensional (7D) autonomous hyperchaotic system, which is obtained by coupling a 1D linear system and a 6D hyperchaotic system that is constructed by adding two linear feedback controllers and a nonlinear feedback controller to the Lorenz system. This hyperchaotic system has very simple algebraic structure but can exhibit complex dynamical behaviors. Of particular interest is that it has a hyperchaotic attractor with five positive Lyapunov exponents and a unique equilibrium in a large range of parameters. Numerical analysis of phase trajectories, Lyapunov exponents, bifurcation, power spectrum and Poincaré projections verifies the existence of hyperchaotic and chaotic attractors. Moreover, stability of the hyperbolic equilibrium is analyzed and a complete mathematical characterization for 7D Hopf bifurcation is given. Finally, circuit experiment implements the hyperchaotic attractor of the 7D system, showing very good agreement with the simulation results.

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Haddadji, Yamina, Mohamed Naguib Harmas, Abdlouahab Bouafia, and Ziyad Bouchama. "Adaptive Terminal Synergetic Synchronization of Hyperchaotic Systems." Journal Européen des Systèmes Automatisés 54, no. 5 (October 31, 2021): 789–95. http://dx.doi.org/10.18280/jesa.540515.

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This research paper introduces an adaptive terminal synergetic nonlinear control. This control aims at synchronizing two hyperchaotic Zhou systems. Thus, the adaptive terminal synergetic control’s synthesis is applied to synchronize a hyperchaotic i.e., slave system with unknown parameters with another hyperchaotic i.e., master system. Accordingly, simulation results of each system in different initial conditions reveal significant convergence. Moreover, the findings proved stability and robustness of the suggested scheme using Lyapunov stability theory.

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Cui, Ning, and Junhong Li. "A new hyperchaotic particle motion system and its control." International Journal of Modern Physics C 30, no. 12 (December 2019): 2050004. http://dx.doi.org/10.1142/s0129183120500047.

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This paper formulates a new hyperchaotic system for particle motion. The continuous dependence on initial conditions of the system’s solution and the equilibrium stability, bifurcation, energy function of the system are analyzed. The hyperchaotic behaviors in the motion of the particle on a horizontal smooth plane are also investigated. It shows that the rich dynamic behaviors of the system, including the degenerate Hopf bifurcations and nondegenerate Hopf bifurcations at multiple equilibrium points, the irregular variation of Hamiltonian energy, and the hyperchaotic attractors. These results generalize and improve some known results about the particle motion system. Furthermore, the constraint of hyperchaos control is obtained by applying Lagrange’s method and the constraint change the system from a hyperchaotic state to asymptotically state. The numerical simulations are carried out to verify theoretical analyses and to exhibit the rich hyperchaotic behaviors.

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John, Siju, and S. N. Kumar. "6D Hyperchaotic Encryption Model for Ensuring Security to 3D Printed Models and Medical Images." Journal of Image and Graphics 12, no. 2 (2024): 117–26. http://dx.doi.org/10.18178/joig.12.2.117-126.

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In the 6G era, where ultra-fast and reliable communication is expected to be ubiquitous, encryption shall continue to play a crucial role in ensuring the security and privacy of data. Encryption and decryption of medical images and 3D printed models using 6D hyperchaotic function is proposed in this research work for ensuring security in data transfer. Here we envisage using a six-dimensional hyperchaotic system for encryption purposes which shall offer a high level of security due to its complex and unpredictable dynamics with multiple positive Lyapunov exponents. This system can potentially enhance the encryption process for 3D objects and medical images, ensuring the protection of sensitive data and preventing unauthorized access. A hyperchaotic system is a type of dynamical system characterized by exhibiting more than one positive Lyapunov exponent, which indicates strong sensitivity to initial conditions. These systems have more degrees of freedom and complex and intricate dynamics compared to standard chaotic systems. The security of the encryption scheme depends on the complexity of the hyperchaotic system and the randomness of the secret key. The parameters of a 6D hyperchaotic system shall be used as an encryption key with six dimensions, each with its range of values, and shall provide many possible keys. In this work, we implemented a 6D hyperchaotic system for the encryption of the 3D printed model and medical images. The performance evaluation was done by metrics entropy, correlation, Number of Pixels Change Rate (NPCR), and Unified Averaged Changed Intensity (UACI) which revealed the robustness of the encryption model in ensuring security. Hyperchaotic systems can be efficiently implemented in parallel computing architectures, which allow faster encryption and decryption processes.

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