Log in

Relevant bibliographies by topics / Chen and Tigan Chaotic systems / Journal articles

To see the other types of publications on this topic, follow the link: Chen and Tigan Chaotic systems.

Journal articles on the topic 'Chen and Tigan Chaotic systems'

Author: Grafiati

Published: 3 June 2025

Last updated: 13 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Chen and Tigan Chaotic systems.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Murugesan, Regan, Suresh Rasappan, Pugalarasu Rajan, and Sathish Kumar Kumaravel. "Synchronization of Liu-Su-Liu and Liu-Chen-Liu Chaotic Systems by Nonlinear Feedback Control." Journal of Computational and Theoretical Nanoscience 16, no. 12 (2019): 4903–7. http://dx.doi.org/10.1166/jctn.2019.8540.

Full text

Abstract:

This paper investigates the global chaos synchronization of identical Liu-Su-Liu chaotic systems (2006) and non-identical Liu-Su-Liu chaotic system (2006) and Liu-Chen-Liu chaotic system (2007). In this paper, active nonlinear control method has been successfully applied to synchronize two identical Liu-Su-Liu chaotic systems and then to synchronize two different chaotic systems, viz. Liu-Su-Liu and Liu-Chen-Liu chaotic systems. Since the Lyapunov exponents are not required for these calculations, the active nonlinear control method is effective and convenient to synchronize Liu-Su-Liu and Liu-Chen-Liu chaotic systems. Numerical simulations are also given to illustrate the proposed synchronization approach.

APA, Harvard, Vancouver, ISO, and other styles

2

Sundarapandian, Vaidyanathan1. "GLOBAL SYNCHRONIZATION OF LÜ-CHEN-CHENG FOUR-SCROLL CHAOTIC SYSTEMS BY SLIDING MODE CONTROL." Computer Science & Engineering: An International Journal (CSEIJ) 1, no. 3 (2019): 26–35. https://doi.org/10.5281/zenodo.3404845.

Full text

Abstract:

This paper investigates the global chaos synchronization of identical Lü-Chen-Cheng four-scroll chaotic systems (Lü, Chen and Cheng, 2004) by sliding mode control. The stability results derived in this paper for the complete synchronization of identical Lü-Chen-Cheng four-scroll chaotic systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Lü-Chen-Cheng four-scroll chaotic systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Lü-Chen-Cheng four-scroll systems

APA, Harvard, Vancouver, ISO, and other styles

3

LÜ, JINHU, GUANRONG CHEN, and SUOCHUN ZHANG. "CONTROLLING IN BETWEEN THE LORENZ AND THE CHEN SYSTEMS." International Journal of Bifurcation and Chaos 12, no. 06 (2002): 1417–22. http://dx.doi.org/10.1142/s0218127402005200.

Full text

Abstract:

This letter investigates a new chaotic system and its role as a joint function between two complex chaotic systems, the Lorenz and the Chen systems, using a simple variable constant controller. With the gradual tuning of the controller, the controlled system evolves from the canonical Lorenz attractor to the Chen attractor through the new transition chaotic attractor. This evolving procedure reveals the forming mechanisms of all similar and closely related chaotic systems, and demonstrates that a simple control technique can be very useful in generating and analyzing some complex chaotic dynamical phenomena.

APA, Harvard, Vancouver, ISO, and other styles

4

VAN GORDER, ROBERT A., and S. ROY CHOUDHURY. "CLASSIFICATION OF CHAOTIC REGIMES IN THE T SYSTEM BY USE OF COMPETITIVE MODES." International Journal of Bifurcation and Chaos 20, no. 11 (2010): 3785–93. http://dx.doi.org/10.1142/s0218127410028033.

Full text

Abstract:

We study chaotic behavior of the T system, a three-dimensional autonomous nonlinear system introduced by G. Tigan [Analysis of a dynamical system derived from the Lorenz system, Sci. Bull. Politehnica Univ Timisoara50 (2005) 61–72] which has potential application in secure communications. The recently-developed technique of competitive modes analysis is applied to determine parameter regimes for which the system may exhibit chaotic behavior. We verify that the T system exhibits interesting behaviors in the many parameter regimes thus obtained, thereby demonstrating the great utility of the competitive modes approach in delineating chaotic regimes in multiparemeter systems, where their identification can otherwise involve tedious numerical searches. An additional, novel finding is that one may use competitive modes "at infinity" in order to identify parameter regimes admitting stable equilibria in dynamical models such as the T system.

APA, Harvard, Vancouver, ISO, and other styles

5

Deng, Xin. "Generating the New Chaotic Attractors of the Lorenz System Family via Anti-Controlling Method." Advanced Materials Research 542-543 (June 2012): 1042–46. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.1042.

Full text

Abstract:

In this paper, the first new chaotic system is gained by anti-controlling Chen system,which belongs to the general Lorenz system; also, the second new chaotic system is gained by anti-controlling the first new chaotic system, which belongs to the general Lü system. Moreover,some basic dynamical properties of two new chaotic systems are studied, either numerically or analytically. The obtained results show clearly that Chen chaotic system and two new chaotic systems also can form another Lorenz system family and deserve further detailed investigation.

APA, Harvard, Vancouver, ISO, and other styles

6

WANG, XIONG, JUAN CHEN, JUN-AN LU, and GUANRONG CHEN. "A SIMPLE YET COMPLEX ONE-PARAMETER FAMILY OF GENERALIZED LORENZ-LIKE SYSTEMS." International Journal of Bifurcation and Chaos 22, no. 05 (2012): 1250116. http://dx.doi.org/10.1142/s0218127412501167.

Full text

Abstract:

This paper reports the finding of a simple one-parameter family of three-dimensional quadratic autonomous chaotic systems. By tuning the only parameter, this system can continuously generate a variety of cascading Lorenz-like attractors, which appears to be richer than the unified chaotic system that contains the Lorenz and the Chen systems as its two extremes. Although this new family of chaotic systems has very rich and complex dynamics, it has a very simple algebraic structure with only two quadratic terms (same as the Lorenz and the Chen systems) and all nonzero coefficients in the linear part being -1 except one -0.1 (thus, simpler than the Lorenz and Chen systems). Surprisingly, although this new system belongs to the Lorenz-type of systems in the classification of the generalized Lorenz canonical form, it can generate not only Lorenz-like attractors but also Chen-like attractors. This suggests that there may exist some other unknown yet more essential algebraic characteristics for describing general three-dimensional quadratic autonomous chaotic systems.

APA, Harvard, Vancouver, ISO, and other styles

7

Sprott, J. C., Xiong Wang, and Guanrong Chen. "When Two Dual Chaotic Systems Shake Hands." International Journal of Bifurcation and Chaos 24, no. 06 (2014): 1450086. http://dx.doi.org/10.1142/s0218127414500862.

Full text

Abstract:

This letter reports an interesting finding that the parametric Lorenz system and the parametric Chen system "shake hands" at a particular point of their common parameter space, as the time variable t → +∞ in the Lorenz system while t → -∞ in the Chen system. This helps better clarify and understand the relationship between these two closely related but topologically nonequivalent chaotic systems.

APA, Harvard, Vancouver, ISO, and other styles

8

SUNDARAPANDIAN, Vaidyanathan, and Karthikeyan RAJAGOPAL. "Anti-Synchronization of Tigan and Li Systems with Unknown Parameters via Adaptive Control." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 2, no. 1 (2011): 17–28. http://dx.doi.org/10.11121/ijocta.01.2012.0076.

Full text

Abstract:

In this paper, we apply adaptive control method toderive new results for the anti-synchronization of identical Tigansystems (2008), identical Li systems (2009) and non-identical Tiganand Li systems. In adaptive anti-synchronization of identical chaoticsystems, the parameters of the master and slave systems are unknownand we devise feedback control law using the estimates of the systemparameters. In adaptive anti-synchronization of non-identical chaoticsystems, the parameters of the master system are known, but theparameters of the slave system are unknown and we devise feedbackcontrol law using the estimates of the parameters of the slave system.Our adaptive synchronization results derived in this paper for theuncertain Tigan and Li systems are established using Lyapunovstability theory. Since the Lyapunov exponents are not required forthese calculations, the adaptive control method is very effective andconvenient to achieve anti-synchronization of identical and nonidenticalTigan and Li systems. Numerical simulations are shown todemonstrate the effectiveness of the adaptive anti-synchronizationschemes for the uncertain chaotic systems addressed in this paper.

APA, Harvard, Vancouver, ISO, and other styles

9

Vaidyanathan, Sundarapandian, and Karthikeyan Rajagopal. "Active Controller Design For Global Choas Anti-Synchronization Of Li and Tigan Chaotic Systems." International Journal of Computer Science and Information Technology 3, no. 4 (2011): 255–68. http://dx.doi.org/10.5121/ijcsit.2011.3420.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

TAM, LAP-MOU, SENG-KIN LAO, LONG-JYE SHEU, and HSIEN-KENG CHEN. "IMPULSIVE SYNCHRONIZATION AND ITS IMPLEMENTATION IN CHEN–LEE SYSTEMS." International Journal of Modern Physics B 25, no. 29 (2011): 3893–903. http://dx.doi.org/10.1142/s0217979211101430.

Full text

Abstract:

The impulsive synchronization of two chaotic Chen–Lee systems was investigated in this paper. Based on Lyapunov's direct method, sufficient conditions for the global exponential synchronization and global asymptotical synchronization were derived. Further, the theoretical results were verified by a numerical simulation. In addition, the impulsive synchronization of two chaotic Chen–Lee systems was also implemented using an electronic circuit.

APA, Harvard, Vancouver, ISO, and other styles

11

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

12

Karthikeyan, Rajagopal, and Vaidyanathan Sundarapandian. "Hybrid Chaos Synchronization of Four–Scroll Systems via Active Control." Journal of Electrical Engineering 65, no. 2 (2014): 97–103. http://dx.doi.org/10.2478/jee-2014-0014.

Full text

Abstract:

Abstract This paper investigates the hybrid chaos synchronization of identical Wang four-scroll systems (Wang, 2009), identical Liu-Chen four-scroll systems (Liu and Chen, 2004) and non-identical Wang and Liu-Chen four-scroll systems. Active control method is the method adopted to achieve the hybrid chaos synchronization of the four-scroll chaotic systems addressed in this paper and our synchronization results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to hybrid synchronize identical and different Wang and Liu-Chen four-scroll chaotic systems. Numerical simulations are also shown to illustrate and validate the hybrid synchronization results derived in this paper.

APA, Harvard, Vancouver, ISO, and other styles

13

YU, PEI, and FEI XU. "A COMMON PHENOMENON IN CHAOTIC SYSTEMS LINKED BY TIME DELAY." International Journal of Bifurcation and Chaos 16, no. 12 (2006): 3727–36. http://dx.doi.org/10.1142/s0218127406017129.

Full text

Abstract:

In this paper, we report a common phenomenon observed in chaotic systems linked by time delay. Recently, the Lorenz chaotic system has been extended to the family of Lorenz systems which includes the Chen and Lü systems. These three chaotic systems, corresponding to different sets of system parameter values, are topologically different. With the aid of numerical simulations, we have surprisingly found that a simple time delay, directly applied to one or more state variables, transforms the Lorenz system to the generalized Chen system or the generalized Lü system without any parameter changes. The existence of this phenomenon has also been found in other known chaotic systems: the Rössler system, the Chua's circuit and the 4-Liu system. This finding has shown a common characteristic of chaotic systems: a new chaotic "branch" can be created from a chaotic attractor by simply adding a time delay.

APA, Harvard, Vancouver, ISO, and other styles

14

WANG, XIONG, and GUANRONG CHEN. "A GALLERY OF LORENZ-LIKE AND CHEN-LIKE ATTRACTORS." International Journal of Bifurcation and Chaos 23, no. 04 (2013): 1330011. http://dx.doi.org/10.1142/s0218127413300115.

Full text

Abstract:

In this article, three-dimensional autonomous chaotic systems with two quadratic terms, similar to the Lorenz system in their algebraic forms, are studied. An attractor with two clearly distinguishable scrolls similar to the Lorenz attractor is referred to as a Lorenz-like attractor, while an attractor with more intertwine between the two scrolls similar to the Chen attractor is referred to as a Chen-like attractor. A gallery of Lorenz-like attractors and Chen-like attractors are presented. For several different families of such systems, through tuning only one real parameter gradually, each of them can generate a spectrum of chaotic attractors continuously changing from a Lorenz-like attractor to a Chen-like attractor. Some intrinsic relationships between the Lorenz system and the Chen system are revealed and discussed. Some common patterns of the Lorenz-like and Chen-like attractors are found and analyzed, which suggest that the instability of the two saddle-foci of such a system somehow determines the shape of its chaotic attractor. These interesting observations on the general dynamic patterns hopefully could shed some light for a better understanding of the intrinsic relationships between the algebraic structures and the geometric attractors of these kinds of chaotic systems.

APA, Harvard, Vancouver, ISO, and other styles

15

Xu, Fei. "A Class of Integer Order and Fractional Order Hyperchaotic Systems via the Chen System." International Journal of Bifurcation and Chaos 26, no. 06 (2016): 1650109. http://dx.doi.org/10.1142/s0218127416501091.

Full text

Abstract:

In this article, we investigate the generation of a class of hyperchaotic systems via the Chen chaotic system using both integer order and fractional order differential equation systems. Based on the Chen chaotic system, we designed a system with four nonlinear ordinary differential equations. For different parameter sets, the trajectory of the system may diverge or display a hyperchaotic attractor with double wings. By linearizing the ordinary differential equation system with divergent trajectory and designing proper switching controls, we obtain a chaotic attractor. Similar phenomenon has also been observed in linearizing the hyperchaotic system. The corresponding fractional order systems are also considered. Our investigation indicates that, switching control can be applied to either linearized chaotic or nonchaotic differential equation systems to create chaotic attractor.

APA, Harvard, Vancouver, ISO, and other styles

16

DONG, PENGZHEN, GANG SHANG, and JIE LIU. "ANTICIPATING SYNCHRONIZATION OF INTEGER ORDER AND FRACTIONAL ORDER HYPER-CHAOTIC CHEN SYSTEM." International Journal of Modern Physics B 26, no. 32 (2012): 1250211. http://dx.doi.org/10.1142/s0217979212502116.

Full text

Abstract:

Such a problem, how to resolve the problem of long-term unpredictability of chaotic systems, has puzzled researchers in nonlinear research fields for a long time during the last decades. Recently, Voss et al. had proposed a new scheme to research the anticipating synchronization of integral-order nonlinear systems for arbitrary initial values and anticipation time. Can this anticipating synchronization be achieved with hyper-chaotic systems? In this paper, we discussed the application of anticipating synchronization in hyper-chaotic systems. Setting integer order and commensurate fractional order hyper-chaotic Chen systems as our research objects, we carry out the research on anticipating synchronization of above two systems based on analyzing the stability of the error system with the Krasovskill–Lyapunov stability theory. Simulation experiments show anticipating synchronization can be achieved in both integer order and fractional order hyper-chaotic Chen system for arbitrary initial value and arbitrary anticipation time.

APA, Harvard, Vancouver, ISO, and other styles

17

LÜ, JINHU, GUANRONG CHEN, DAIZHAN CHENG, and SERGEJ CELIKOVSKY. "BRIDGE THE GAP BETWEEN THE LORENZ SYSTEM AND THE CHEN SYSTEM." International Journal of Bifurcation and Chaos 12, no. 12 (2002): 2917–26. http://dx.doi.org/10.1142/s021812740200631x.

Full text

Abstract:

This paper introduces a unified chaotic system that contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum. The new system represents the continued transition from the Lorenz to the Chen system and is chaotic over the entire spectrum of the key system parameter. Dynamical behaviors of the unified system are investigated in somewhat detail.

APA, Harvard, Vancouver, ISO, and other styles

18

Nuñez-Perez, Jose-Cruz, Vincent-Ademola Adeyemi, Yuma Sandoval-Ibarra, Francisco-Javier Perez-Pinal, and Esteban Tlelo-Cuautle. "Maximizing the Chaotic Behavior of Fractional Order Chen System by Evolutionary Algorithms." Mathematics 9, no. 11 (2021): 1194. http://dx.doi.org/10.3390/math9111194.

Full text

Abstract:

This paper presents the application of three optimization algorithms to increase the chaotic behavior of the fractional order chaotic Chen system. This is achieved by optimizing the maximum Lyapunov exponent (MLE). The applied optimization techniques are evolutionary algorithms (EAs), namely: differential evolution (DE), particle swarm optimization (PSO), and invasive weed optimization (IWO). In each algorithm, the optimization process is performed using 100 individuals and generations from 50 to 500, with a step of 50, which makes a total of ten independent runs. The results show that the optimized fractional order chaotic Chen systems have higher maximum Lyapunov exponents than the non-optimized system, with the DE giving the highest MLE. Additionally, the results indicate that the chaotic behavior of the fractional order Chen system is multifaceted with respect to the parameter and fractional order values. The dynamical behavior and complexity of the optimized systems are verified using properties, such as bifurcation, LE spectrum, equilibrium point, eigenvalue, and sample entropy. Moreover, the optimized systems are compared with a hyper-chaotic Chen system on the basis of their prediction times. The results show that the optimized systems have a shorter prediction time than the hyper-chaotic system. The optimized results are suitable for developing a secure communication system and a random number generator. Finally, the Halstead parameters measure the complexity of the three optimization algorithms that were implemented in MATLAB. The results reveal that the invasive weed optimization has the simplest implementation.

APA, Harvard, Vancouver, ISO, and other styles

19

ČELIKOVSKÝ, SERGEJ, and GUANRONG CHEN. "ON A GENERALIZED LORENZ CANONICAL FORM OF CHAOTIC SYSTEMS." International Journal of Bifurcation and Chaos 12, no. 08 (2002): 1789–812. http://dx.doi.org/10.1142/s0218127402005467.

Full text

Abstract:

This paper shows that a large class of systems, introduced in [Čelikovský & Vaněček, 1994; Vaněček & Čelikovský, 1996] as the so-called generalized Lorenz system, are state-equivalent to a special canonical form that covers a broader class of chaotic systems. This canonical form, called generalized Lorenz canonical form hereafter, generalizes the one introduced and analyzed in [Čelikovský & Vaněček, 1994; Vaněček & Čelikovský, 1996], and also covers the so-called Chen system, recently introduced in [Chen & Ueta, 1999; Ueta & Chen, 2000].Thus, this new generalized Lorenz canonical form contains as special cases the original Lorenz system, the generalized Lorenz system, and the Chen system, so that a comparison of the structures between two essential types of chaotic systems becomes possible. The most important property of the new canonical form is the parametrization that has precisely a single scalar parameter useful for chaos tuning, which has promising potential in future engineering chaos design. Some other closely related topics are also studied and discussed in the paper.

APA, Harvard, Vancouver, ISO, and other styles

20

Matouk, A. E. "Chaos Synchronization between Two Different Fractional Systems of Lorenz Family." Mathematical Problems in Engineering 2009 (2009): 1–11. http://dx.doi.org/10.1155/2009/572724.

Full text

Abstract:

This work investigates chaos synchronization between two different fractional order chaotic systems of Lorenz family. The fractional order Lü system is controlled to be the fractional order Chen system, and the fractional order Chen system is controlled to be the fractional order Lorenz-like system. The analytical conditions for the synchronization of these pairs of different fractional order chaotic systems are derived by utilizing Laplace transform. Numerical simulations are used to verify the theoretical analysis using different values of the fractional order parameter.

APA, Harvard, Vancouver, ISO, and other styles

21

Sprott, J. C. "New Chaotic Regimes in the Lorenz and Chen Systems." International Journal of Bifurcation and Chaos 25, no. 02 (2015): 1550033. http://dx.doi.org/10.1142/s0218127415500339.

Full text

Abstract:

It has recently been shown that the Chen system with c > 0 is identical to the reversed-time Lorenz system with particular negative parameters and that the Chen system with c < 0 is identical to the forward-time Lorenz system with particular negative parameters. This note describes this new regime and shows that it admits chaotic solutions that were previously unexplored in either system.

APA, Harvard, Vancouver, ISO, and other styles

22

SARASOLA, C., A. D'ANJOU, F. J. TORREALDEA, and A. MOUJAHID. "ENERGY-LIKE FUNCTIONS FOR SOME DISSIPATIVE CHAOTIC SYSTEMS." International Journal of Bifurcation and Chaos 15, no. 08 (2005): 2507–21. http://dx.doi.org/10.1142/s0218127405013447.

Full text

Abstract:

Functions of the phase space variables that can considered as possible energy functions for a given family of dissipative chaotic systems are discussed. This kind of functions are interesting due to their use as an energy-like quantitative measure to characterize different aspects of dynamic behavior of associated chaotic systems. We have calculated quadratic energy-like functions for the cases of Lorenz, Chen, Lü–Chen and Chua, and show the patterns of dissipation of energy on their respective attractors. We also show that in the case of the Rössler system at least a fourth-order polynomial is required to properly represent its energy.

APA, Harvard, Vancouver, ISO, and other styles

23

Zhi, Li, and Han Chong-Zhao. "Adaptive synchronization of Rossler and Chen chaotic systems." Chinese Physics 11, no. 7 (2002): 666–69. http://dx.doi.org/10.1088/1009-1963/11/7/304.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

ZHAO, JIAKUN, YING WU, and YUYING WANG. "ADAPTIVE FUNCTION Q-S SYNCHRONIZATION OF DIFFERENT CHAOTIC (HYPER-CHAOTIC) SYSTEMS." International Journal of Modern Physics B 27, no. 20 (2013): 1350109. http://dx.doi.org/10.1142/s0217979213501099.

Full text

Abstract:

This paper presents the general method for the adaptive function Q-S synchronization of different chaotic (hyper-chaotic) systems. Based upon the Lyapunov stability theory, the dynamical evolution can be achieved by the Q-S synchronization with a desired scaling function between the different chaotic (hyper-chaotic) systems. This approach is successfully applied to two examples: Chen hyper-chaotic system drives the Lorenz hyper-chaotic system; Lorenz system drives Lü hyper-chaotic system. Numerical simulations are used to validate and demonstrate the effectiveness of the proposed scheme.

APA, Harvard, Vancouver, ISO, and other styles

25

Shen, Yupeng, Tao Zou, Lei Zhang, Zhao Wu, Yanrui Su, and Fabao Yan. "A novel solar radio spectrogram encryption algorithm based on parameter variable chaotic systems and DNA dynamic encoding." Physica Scripta 97, no. 5 (2022): 055210. http://dx.doi.org/10.1088/1402-4896/ac65bf.

Full text

Abstract:

Abstract Considering that chaotic systems are highly sensitive to parameters, we design two new parameter variable chaotic systems by constructing parameter perturbation items. These systems are constructed using the state variables of the Liu chaotic system to perturb the parameters of the Lorenz and Chen chaotic systems and are called the Lorenz-Liu chaotic system (LLCS) and Chen-Liu chaotic system (CLCS), respectively. In particular, the parameter perturbation items constructed in this study are not periodic but rather chaotic signals and change in real time. Compared with the original systems, they exhibit more complex randomness and dynamic behaviors. In the proposed cryptosystem, which considers the concept of Deoxyribonucleic Acid (DNA), the solar radio spectrogram is dynamically encoded through the LLCS, and then, the CLCS is used to scramble and diffuse the decoding matrices. In addition, the algorithm uses the 256-bit Secure Hash Algorithm (SHA-256) to generate the initial keys, which enhances the algorithm’s sensitivity to plaintext. Simulation results and security analysis show that the cryptosystem has a large key space and high key sensitivity, and can resist various attacks, such as differential attacks and chosen-plaintext attacks.

APA, Harvard, Vancouver, ISO, and other styles

26

YU, YONG-GUANG, HAN-XIONG LI, and JUN-ZHI YU. "THE HYBRID FUNCTION PROJECTIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS." International Journal of Modern Physics C 20, no. 05 (2009): 789–97. http://dx.doi.org/10.1142/s0129183109013972.

Full text

Abstract:

This paper mainly investigated a hybrid function projective synchronization of two different chaotic systems. Based on the Lyapunov stability theory, an adaptive controller for the synchronization of two different chaotic systems is designed. This technique is applied to achieve the synchronization between Lorenz and Rössler chaotic systems, and the synchronization of hyperchaotic Rössler and Chen systems. The numerical simulation results illustrate the effectiveness and feasibility of the proposed scheme.

APA, Harvard, Vancouver, ISO, and other styles

27

BAO, BOCHENG, ZHONG LIU, and JUEBANG YU. "MODIFIED GENERALIZED LORENZ SYSTEM AND FOLDED CHAOTIC ATTRACTORS." International Journal of Bifurcation and Chaos 19, no. 08 (2009): 2573–87. http://dx.doi.org/10.1142/s0218127409024323.

Full text

Abstract:

A modified generalized Lorenz system in a canonical form extended from the generalized Lorenz system is proposed in this paper. This novel system has a folded factor and can display complex 2-scroll folded attractors and 1-scroll folded attractors at different parameter values. Three typical normal forms, called Lorenz-like, Chen-like and Lü-like chaotic system respectively, of three-dimensional quadratic autonomous chaotic systems are derived, and their dynamical behaviors are further investigated by employing Lyapunov exponent spectrum, bifurcation diagram, Poincaré mapping and phase portrait, etc. Of particular interest is the fact that the folded factor makes Chen-like and Lü-like chaotic systems exhibit complicated nonlinear dynamical phenomena.

APA, Harvard, Vancouver, ISO, and other styles

28

Wu, Xian Yong, Hao Wu, and Hao Gong. "Chaos Anti-Synchronization between Chen System and Lu System." Applied Mechanics and Materials 631-632 (September 2014): 710–13. http://dx.doi.org/10.4028/www.scientific.net/amm.631-632.710.

Full text

Abstract:

Anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen and Lu systems to demonstrate the effectiveness of the proposed control strategy.

APA, Harvard, Vancouver, ISO, and other styles

29

Tian, Anhong, Chengbiao Fu, Her-Terng Yau, Xiao-Yi Su, and Heigang Xiong. "Soil Salinization Level Monitoring and Classifying by Mixed Chaotic Systems." Remote Sensing 13, no. 19 (2021): 3819. http://dx.doi.org/10.3390/rs13193819.

Full text

Abstract:

Soil salinization process is a complex non-linear dynamic evolution. To classify a system with this type of non-linear characteristic, this study proposed a mixed master/slave chaotic system based on Chua’s circuit and a fractional-order Chen-Lee chaotic system to classify soil salinization level. The subject is the soil in Xinjiang with different levels of human interference. A fractional-order Chen-Lee chaotic system was constructed, and the spectral signal processed by the Chua’s non-linear circuit was substituted into the master/slave chaotic system. The chaotic dynamic errors with different fractional orders were calculated. The comparative analysis showed that 0.1-order has the largest chaotic dynamic error change, which produced two distinct and divergent results. Thus, this study converted the chaotic dynamic errors of fractional 0.1-order into chaotic attractors to build an extension matter-element model. Finally, we compared the soil salt contents (SSC) from the laboratory chemical analysis with the results of the extension theory classification. The comparison showed that the combination of fractional order mixed master/slave chaotic system and extension theory has high classification accuracy for soil salinization level. The results of this system match the result of the chemical analysis. The classification accuracy of the calibration set data was 100%, and the classification accuracy of the validation set data was 90%. This method is the first use of the mixed master/slave chaotic system in this field and can satisfy certain soil salinization monitoring needs as well as promote the application of the chaotic system in soil salinization monitoring.

APA, Harvard, Vancouver, ISO, and other styles

30

Kim, Eunro, Inseok Yang, and Dongik Lee. "Time-Delay Robust Nonlinear Dynamic Inversion for Chaos Synchronization with Application to Secure Communications." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/651950.

Full text

Abstract:

The time-delay robust nonlinear dynamic inversion (TDRNDI) control technique is proposed to synchronize time-delay Chen systems. The time-delay Chen circuit is simple but exhibits complex irregular (chaotic) behavior. For this reason, this circuit can be efficiently used to encrypt messages for secure communication. In this paper, the nonlinear control-based chaos synchronization problem is considered. The proposed TDRNDI controller is a modified version of a robust nonlinear dynamic inversion (RNDI) applicable to chaotic systems, including time-delay systems. The performance and feasibility of the proposed TDRNDI controller are demonstrated by conducting numerical simulations with application to a secure communication network.

APA, Harvard, Vancouver, ISO, and other styles

31

Rosalie, Martin. "Templates of Two Foliated Attractors — Lorenz and Chen Systems." International Journal of Bifurcation and Chaos 26, no. 02 (2016): 1650037. http://dx.doi.org/10.1142/s0218127416500371.

Full text

Abstract:

A chaotic attractor solution of the Lorenz system [Lorenz, 1963] with foliated structure is topologically characterized. Its template permits to both summarize the organization of its periodic orbits and detail the topology of the solution as a branched manifold. A template of an attractor solution of the Chen system [Chen & Ueta, 1999] with a similar foliated structure is also established.

APA, Harvard, Vancouver, ISO, and other styles

32

Li, Ying Kui. "The Synchronization of Super-Chen Chaotic Scheme with a Sort of Oscillating Parameters." Advanced Materials Research 282-283 (July 2011): 612–15. http://dx.doi.org/10.4028/www.scientific.net/amr.282-283.612.

Full text

Abstract:

Most properties of Super Chen’s chaotic system satisfy with the requirements of secure communication and cryptography. Implusive stabilzation for control and synchronization of Super Chen’s chaotic systems can be applied in secure communication. Super Chen’s Chaotic synchronization control can be the kernel technology in chaos-based secure commu-nication. In this paper we propose a hybrid Super Chen chaotic synchronization scheme control which contains both continuous chaotic system with a sort of oscillating parameters and discrete chaotic system. If oscillating parameters approach to 0, we proved that two systems can get synchronized without control signal transmitting.

APA, Harvard, Vancouver, ISO, and other styles

33

WANG, XINGYUAN, and YONG WANG. "ANTI-SYNCHRONIZATION OF THREE-DIMENSIONAL AUTONOMOUS CHAOTIC SYSTEMS VIA ACTIVE CONTROL." International Journal of Modern Physics B 21, no. 17 (2007): 3017–27. http://dx.doi.org/10.1142/s0217979207037508.

Full text

Abstract:

This paper analyzes anti-synchronization of three-dimensional autonomous chaotic systems and achieves the anti-synchronization of a class of three-dimensional autonomous chaotic systems, i.e., Lorenz system, Chen system, and Lü system with one another via active control. Numerical simulations are demonstrated to verify the effectiveness of the proposed method.

APA, Harvard, Vancouver, ISO, and other styles

34

ZHAO, JIAKUN, and YING WU. "FUNCTION PROJECTIVE SYNCHRONIZATION OF THE CHAOTIC SYSTEMS WITH PARAMETERS UNKNOWN." International Journal of Modern Physics B 27, no. 21 (2013): 1350110. http://dx.doi.org/10.1142/s0217979213501105.

Full text

Abstract:

This work is concerned with the general methods for the function projective synchronization (FPS) of chaotic (or hyperchaotic) systems. The aim is to investigate the FPS of different chaotic (hyper-chaotic) systems with unknown parameters. The adaptive control law and the parameter update law are derived to make the states of two different chaotic systems asymptotically synchronized up to a desired scaling function by Lyapunov stability theory. The general approach for FPS of Chen hyperchaotic system and Lü system is provided. Numerical simulations are also presented to verify the effectiveness of the proposed scheme.

APA, Harvard, Vancouver, ISO, and other styles

35

Lin, Jui-sheng, Neng-Sheng Pai, and Her-Terng Yau. "Robust Controller Design for Modified Projective Synchronization of Chen-Lee Chaotic Systems with Nonlinear Inputs." Mathematical Problems in Engineering 2009 (2009): 1–10. http://dx.doi.org/10.1155/2009/649401.

Full text

Abstract:

This study demonstrates the modified projective synchronization in Chen-Lee chaotic system. The variable structure control technology is used to design the synchronization controller with input nonlinearity. Based on Lyapunov stability theory, a nonlinear controller and some generic sufficient conditions can be obtained to guarantee the modified projective synchronization, including synchronization, antisynchronization, and projective synchronization in spite of the input nonlinearity. The numerical simulation results show that the synchronization and antisynchronization can coexist in Chen-Lee chaotic systems. It demonstrates the validity and feasibility of the proposed controller.

APA, Harvard, Vancouver, ISO, and other styles

36

Esen, Oğul, Anindya Ghose Choudhury, and Partha Guha. "Bi-Hamiltonian Structures of 3D Chaotic Dynamical Systems." International Journal of Bifurcation and Chaos 26, no. 13 (2016): 1650215. http://dx.doi.org/10.1142/s0218127416502151.

Full text

Abstract:

We study Hamiltonian structures of dynamical systems with three degrees of freedom which are known for their chaotic properties, namely Lü, modified Lü, Chen, [Formula: see text] and Qi systems. We show that all these flows admit bi-Hamiltonian structures depending on the values of their parameters.

APA, Harvard, Vancouver, ISO, and other styles

37

Liu, Shu Bo, Shu Min Zhou, and Li Yong Hu. "Output Tracking Control and Synchronization of Continuous Chaotic Systems Using Differential Evolution Algorithm." Applied Mechanics and Materials 37-38 (November 2010): 823–28. http://dx.doi.org/10.4028/www.scientific.net/amm.37-38.823.

Full text

Abstract:

This paper applies differential evolution (DE) algorithm to realize the output tracking control and synchronization of continuous chaotic systems. The output tracking control of single-input single-output (SISO) and multi-input multi-output (MIMO) chaotic system is investigated. Moreover, synchronization of chaotic systems with parameter mismatch or structure difference is also under discussion. Numerical simulations based on the well-known models such as Lorenz and Chen systems are used to illustrate the validity of this theoretical method.

APA, Harvard, Vancouver, ISO, and other styles

38

Yang, Chunde, Hao Cai, and Ping Zhou. "Compound Generalized Function Projective Synchronization for Fractional-Order Chaotic Systems." Discrete Dynamics in Nature and Society 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/7563416.

Full text

Abstract:

A modified function projective synchronization for fractional-order chaotic system, called compound generalized function projective synchronization (CGFPS), is proposed theoretically in this paper. There are one scaling-drive system, more than one base-drive system, and one response system in the scheme of CGFPS, and the scaling function matrices come from multidrive systems. The proposed CGFPS technique is based on the stability theory of fractional-order system. Moreover, we achieve the CGFPS between three-driver chaotic systems, that is, the fractional-order Arneodo chaotic system, the fractional-order Chen chaotic system, and the fractional-order Lu chaotic system, and one response chaotic system, that is, the fractional-order Lorenz chaotic system. Numerical experiments are demonstrated to verify the effectiveness of the CGFPS scheme.

APA, Harvard, Vancouver, ISO, and other styles

39

ODIBAT, ZAID M., NATHALIE CORSON, M. A. AZIZ-ALAOUI, and CYRILLE BERTELLE. "SYNCHRONIZATION OF CHAOTIC FRACTIONAL-ORDER SYSTEMS VIA LINEAR CONTROL." International Journal of Bifurcation and Chaos 20, no. 01 (2010): 81–97. http://dx.doi.org/10.1142/s0218127410025429.

Full text

Abstract:

The chaotic dynamics of fractional-order systems has attracted much attention recently. Chaotic synchronization of fractional-order systems is further studied in this paper. We investigate the chaos synchronization of two identical systems via a suitable linear controller applied to the response system. Based on the stability results of linear fractional-order systems, sufficient conditions for chaos synchronization of these systems are given. Control laws are derived analytically to achieve synchronization of the chaotic fractional-order Chen, Rössler and modified Chua systems. Numerical simulations are provided to verify the theoretical analysis.

APA, Harvard, Vancouver, ISO, and other styles

40

Li, Zhi, Chongzhao Han, and Songjiao Shi. "Modification for synchronization of Rossler and Chen chaotic systems." Physics Letters A 301, no. 3-4 (2002): 224–30. http://dx.doi.org/10.1016/s0375-9601(02)00970-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Wang, Junwei, Xiaohua Xiong, and Yanbin Zhang. "Extending synchronization scheme to chaotic fractional-order Chen systems." Physica A: Statistical Mechanics and its Applications 370, no. 2 (2006): 279–85. http://dx.doi.org/10.1016/j.physa.2006.03.021.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Sun, Yeong-Jeu. "A simple observer of the generalized Chen chaotic systems." Chaos, Solitons & Fractals 39, no. 4 (2009): 1641–44. http://dx.doi.org/10.1016/j.chaos.2007.06.043.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

EL-KHAZALI, REYAD, WAJDI AHMAD, and YOUSEF AL-ASSAF. "SLIDING MODE CONTROL OF GENERALIZED FRACTIONAL CHAOTIC SYSTEMS." International Journal of Bifurcation and Chaos 16, no. 10 (2006): 3113–25. http://dx.doi.org/10.1142/s0218127406016719.

Full text

Abstract:

A sliding mode control technique is introduced for generalized fractional chaotic systems. These systems are governed by a set of fractional differential equations of incommensurate orders. The proposed design method relies on the fact that the stability region of a fractional system contains the stability region of its underlying integer-order model. A sliding mode controller designed for an equivalent integer-order chaotic system is used to stabilize all its corresponding fractional chaotic systems. The design technique is demonstrated using two generalized fractional chaotic models; a chaotic oscillator and the Chen system. The effect of the total fractional order is investigated with respect to the controller effort and the convergence rate of the system response to the origin. Numerical simulations validate the main results of this work.

APA, Harvard, Vancouver, ISO, and other styles

44

Méndez-Ramírez, Rodrigo, Adrian Arellano-Delgado, Miguel Murillo-Escobar, and César Cruz-Hernández. "Degradation Analysis of Chaotic Systems and their Digital Implementation in Embedded Systems." Complexity 2019 (December 4, 2019): 1–22. http://dx.doi.org/10.1155/2019/9863982.

Full text

Abstract:

Digital implementation of chaotic systems (CSs) has attracted increasing attention from researchers due to several applications in engineering, e.g., in areas as cryptography and autonomous mobile robots, where the properties of chaotic systems are strongly related. The CSs in the continuous version (CV) need to be discretized where chaotic degradation must be analyzed to guarantee preservation of chaos. In this paper, we present a degradation analysis of five three-dimensional CSs and the necessary conditions to implement the discretized versions (DVs) of Lorenz, Rössler, Chen, Liu and Chen, and Méndez-Arellano-Cruz-Martínez (MACM) CSs. Analytical and numerical analyses of chaos degradation are conducted by using the time series method; the maximum discrete step size and the Lyapunov Exponents (LEs) are computed by using the Euler, Heun, and fourth-order Runge–Kutta (RK4) numerical algorithms (NAs). We conducted comparative studies of performance based on time complexity of the five proposed CSs in their DVs by using four embedded systems (ESs) based on three families of Microchip microcontrollers 8-bit PIC16F, 16-bit dsPIC33FJ, and 32-bit PIC32MZ (of low-cost electronic implementation) and a Field Programmable Gate Array (FPGA). Based on the results, the intervals at control parameters to guarantee chaos are proposed, which improves the performance characteristics of the five proposed CSs in their DVs based on digital applications.

APA, Harvard, Vancouver, ISO, and other styles

45

Zhou, Ping, Rui Ding, and Yu-xia Cao. "Hybrid Projective Synchronization for Two Identical Fractional-Order Chaotic Systems." Discrete Dynamics in Nature and Society 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/768587.

Full text

Abstract:

A hybrid projective synchronization scheme for two identical fractional-order chaotic systems is proposed in this paper. Based on the stability theory of fractional-order systems, a controller for the synchronization of two identical fractional-order chaotic systems is designed. This synchronization scheme needs not to absorb all the nonlinear terms of response system. Hybrid projective synchronization for the fractional-order Chen chaotic system and hybrid projective synchronization for the fractional-order hyperchaotic Lu system are used to demonstrate the validity and feasibility of the proposed scheme.

APA, Harvard, Vancouver, ISO, and other styles

46

Donia, Fadhil Chalob, Abdulbaqi Maryoosh Amal, Mohammed Essa Zainab, and Nassir Abbud Elaf. "A new block cipher for image encryption based on multi chaotic systems." TELKOMNIKA Telecommunication, Computing, Electronics and Control 18, no. 6 (2020): 2983~2991. https://doi.org/10.12928/TELKOMNIKA.v18i6.13746.

Full text

Abstract:

In this paper, a new algorithm for image encryption is proposed based on three chaotic systems which are Chen system, logistic map and two-dimensional (2D) Arnold cat map. First, a permutation scheme is applied to the image, and then shuffled image is partitioned into blocks of pixels. For each block, Chen system is employed for confusion and then logistic map is employed for generating subsititution-box (S-box) to substitute image blocks. The S-box is dynamic, where it is shuffled for each image block using permutation operation. Then, 2D Arnold cat map is used for providing diffusion, after that XORing the result using Chen system to obtain the encrypted image. The high security of proposed algorithm is experimented using histograms, unified average changing intensity (UACI), number of pixels change rate (NPCR), entropy, correlation and key space analyses.

APA, Harvard, Vancouver, ISO, and other styles

47

SHI, YUMING, PEI YU, and GUANRONG CHEN. "CHAOTIFICATION OF DISCRETE DYNAMICAL SYSTEMS IN BANACH SPACES." International Journal of Bifurcation and Chaos 16, no. 09 (2006): 2615–36. http://dx.doi.org/10.1142/s021812740601629x.

Full text

Abstract:

This paper is concerned with chaotification of discrete dynamical systems in Banach spaces via feedback control techniques. A criterion of chaos in Banach spaces is first established. This criterion extends and improves the Marotto theorem. Discussions are carried out in general and some special Banach spaces. All the controlled systems are proved to be chaotic in the sense of both Devaney and Li–Yorke. As a consequence, a controlled system described in a finite-dimensional real space studied by Wang and Chen is shown chaotic not only in the sense of Li–Yorke but also in the sense of Devaney. The original system can be driven to be chaotic by using an arbitrarily small-amplitude state feedback control in a certain space. In addition, the Chen–Lai anti-control algorithm via feedback control with mod-operation in a finite-dimensional real space is extended to a certain infinite-dimensional Banach space, and the controlled system is shown chaotic in the sense of Devaney as well as in the sense of both Li–Yorke and Wiggins. Differing from many existing results, it is not here required that the map corresponding to the original system has a fixed point in some cases. An application of the theoretical results to a class of first-order partial difference equations is given with some numerical simulations.

APA, Harvard, Vancouver, ISO, and other styles

48

Li, Chunlai, Lei Wu, Hongmin Li, and Yaonan Tong. "A novel chaotic system and its topological horseshoe." Nonlinear Analysis: Modelling and Control 18, no. 1 (2013): 66–77. http://dx.doi.org/10.15388/na.18.1.14032.

Full text

Abstract:

Based on the construction pattern of Chen, Liu and Qi chaotic systems, a new threedimensional (3D) chaotic system is proposed by developing Lorenz chaotic system. It’s found that when parameter e varies, the Lyapunov exponent spectrum keeps invariable, and the signal amplitude can be controlled by adjusting e. Moreover, the horseshoe chaos in this system is investigated based on the topological horseshoe theory.

APA, Harvard, Vancouver, ISO, and other styles

49

Almutairi, Najat. "An application of fractal fractional operators to non-linear Chen systems." Thermal Science 28, no. 6 Part B (2024): 5169–78. https://doi.org/10.2298/tsci2406169a.

Full text

Abstract:

This paper employs the Atangana-Baleanu fractal-fractional operators to establish whether chaotic behavior is present or not in a non-linear modified Chen. The Chen exists and is unique under fixed point theory. To illustrate the applicability and efficiency of this method, numerical examples are provided to provide a better understanding of it. To verify the results in this paper, a circuit schematic has been drawn and a simulation has been conducted.

APA, Harvard, Vancouver, ISO, and other styles

50

Xu, Fei. "Integer and Fractional Order Multiwing Chaotic Attractors via the Chen System and the Lü System with Switching Controls." International Journal of Bifurcation and Chaos 24, no. 03 (2014): 1450029. http://dx.doi.org/10.1142/s0218127414500291.

Full text

Abstract:

In this work, we investigate the generation of multiwing chaotic attractors using integer and fractional order linear differential equation systems with switching controls. Based on the properties of the Chen system and the Lü system, a series of switching control strategies are proposed to link two linearized, integer or fractional order such systems. Numerical simulation results indicate that the controlled systems exhibit a variety of rich dynamical behaviors including multiwing and grid multiwing chaotic attractors.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!