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Journal articles on the topic 'New chaotic reversal system'

Author: Grafiati

Published: 4 June 2025

Last updated: 1 August 2025

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1

S. Ojoniyi, Olurotimi. "Function Projective Synchronization of New Chaotic Reversal Systems." International Journal of Computer Science, Engineering and Information Technology 4, no. 5 (2014): 33–39. http://dx.doi.org/10.5121/ijcseit.2014.4503.

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2

Li, Chunbiao, Julien Clinton Sprott, and Yongjian Liu. "Time-Reversible Chaotic System with Conditional Symmetry." International Journal of Bifurcation and Chaos 30, no. 05 (2020): 2050067. http://dx.doi.org/10.1142/s0218127420500674.

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When the polarity reversal induced by offset boosting is considered, a new regime of a time-reversible chaotic system with conditional symmetry is found, and some new time-reversible systems are revealed based on multiple dimensional offset boosting. Numerical analysis shows that the system attractor and repellor have their own dynamics in respective time domains which constitutes the fundamental property in a time-reversible system. More remarkably, when the conditional symmetry is destroyed by a slightly mismatched offset controller, the system undergoes different bifurcations to chaos, and

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3

Bakri, Taoufik, and Ferdinand Verhulst. "Time-reversal, tori families,\query{Q1} and canards in the Sprott A and NE9 systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 8 (2022): 083119. http://dx.doi.org/10.1063/5.0097508.

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Quadratic three-dimensional autonomous systems may display complex behavior. Studying the systems Sprott A and NE9, we find families of tori and periodic solutions both involving canards. Using time-reversal and symmetry, we are able to explain in these two systems both the analysis and origin of tori, periodic solutions, and the numerics of these objects. For system NE9, unbounded solutions exist that admit analytic description by singular perturbation theory of the flow near infinity, also we observe torus destruction and a new chaotic attractor (Kaplan–Yorke dimension 2.1544) produced by a

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4

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.

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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.

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Chakraborty, Saumen, Manaj Dandapathak, and Saumendra Sankar De Sarkar. "Effect of Self Feedback on Mean-Field Coupled Oscillators: Revival and Quenching of Oscillations." International Journal of Bifurcation and Chaos 31, no. 05 (2021): 2150078. http://dx.doi.org/10.1142/s0218127421500784.

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Interaction among different units in a network of oscillators may often lead to quenching of oscillations and the importance of oscillation quenching can be found in controlling the dynamics of many real world systems. But there are also many real life phenomena where suppression of oscillation should be avoided for maintaining the sustained evolution of the system. In this work, we propose a self-feedback control scheme through which one is able to either achieve quenching or to retrieve the rhythmic behavior in a network of mean-field diffusively coupled systems. It is found that for proper

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6

Feng, Chunsheng, Lijie Li, Yongjian Liu, and Zhouchao Wei. "Global Dynamics of the Chaotic Disk Dynamo System Driven by Noise." Complexity 2020 (March 26, 2020): 1–9. http://dx.doi.org/10.1155/2020/8375324.

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The disk dynamo system, which is capable of chaotic behaviours, is obtained experimentally from two disk dynamos connected together. It models the geomagnetic field and is used to explain the reversals in its polarity. Actually, the parameters of the chaotic systems exhibit random fluctuation to a greater or lesser extent, which can carefully describe the disturbance made by environmental noise. The global dynamics of the chaotic disk dynamo system with random fluctuating parameters are concerned, and some new results are presented. Based on the generalized Lyapunov function, the globally attr

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7

DOWNAROWICZ, TOMASZ, and YVES LACROIX. "Measure-theoretic chaos." Ergodic Theory and Dynamical Systems 34, no. 1 (2012): 110–31. http://dx.doi.org/10.1017/etds.2012.117.

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AbstractWe define new isomorphism invariants for ergodic measure-preserving systems on standard probability spaces, called measure-theoretic chaos and measure-theoretic$^+$ chaos. These notions are analogs of the topological chaos DC2 and its slightly stronger version (which we denote by $\text {DC}1\frac 12$). We prove that: (1) if a topological system is measure-theoretically (measure-theoretically$^+$) chaotic with respect to at least one of its ergodic measures then it is topologically DC2 $(\text {DC}1\frac 12)$ chaotic; (2) every ergodic system with positive Kolmogorov–Sinai entropy is m

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8

Li, Shih-Yu, Cheng-Hsiung Yang, Li-Wei Ko, Chin-Teng Lin, and Zheng-Ming Ge. "Implementation on Electronic Circuits and RTR Pragmatical Adaptive Synchronization: Time-Reversed Uncertain Dynamical Systems' Analysis and Applications." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/909721.

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We expose the chaotic attractors of time-reversed nonlinear system, further implement its behavior on electronic circuit, and apply the pragmatical asymptotically stability theory to strictly prove that the adaptive synchronization of given master and slave systems with uncertain parameters can be achieved. In this paper, the variety chaotic motions of time-reversed Lorentz system are investigated through Lyapunov exponents, phase portraits, and bifurcation diagrams. For further applying the complex signal in secure communication and file encryption, we construct the circuit to show the simila

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9

Wang, Zhen Chao, Shi Bing Zhang, and Yuan Yuan Liu. "A Noise Eliminating Method of DCSK System Based on Multi-Layered Noise Control Materials." Advanced Materials Research 461 (February 2012): 164–68. http://dx.doi.org/10.4028/www.scientific.net/amr.461.164.

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This paper proposes a new chaotic communication scheme which is developed from Differential Chaos Shift Keying (DCSK), named reversed-phase overlay DCSK. Different from DCSK, at the receiver of the improved scheme the first and the second half-symbol signals within a code period are reversed-phase overlapped before the correlation operation. Both the theoretical analysis and the simulation results show that the proposed scheme can effectively suppress the noise and improve the BER performance of DCSK if the channel noise in the first half of a code period and the second is positively correlate

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10

Westerhold, Thomas, Ursula Röhl, Thomas Frederichs, et al. "Astronomical calibration of the Ypresian timescale: implications for seafloor spreading rates and the chaotic behavior of the solar system?" Climate of the Past 13, no. 9 (2017): 1129–52. http://dx.doi.org/10.5194/cp-13-1129-2017.

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Abstract. To fully understand the global climate dynamics of the warm early Eocene with its reoccurring hyperthermal events, an accurate high-fidelity age model is required. The Ypresian stage (56–47.8 Ma) covers a key interval within the Eocene as it ranges from the warmest marine temperatures in the early Eocene to the long-term cooling trends in the middle Eocene. Despite the recent development of detailed marine isotope records spanning portions of the Ypresian stage, key records to establish a complete astronomically calibrated age model for the Ypresian are still missing. Here we present

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11

Pop-Eleches, Grigore. "Throwing out the Bums: Protest Voting and Unorthodox Parties after Communism." World Politics 62, no. 2 (2010): 221–60. http://dx.doi.org/10.1017/s0043887110000043.

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The electoral rise of unorthodox parties (UOPs) in recent East European elections raises some puzzling questions about electoral dynamics in new democracies. Why did the power alternation of the mid-1990s not result in party-system consolidation, as suggested by some earlier studies, but instead give way to a much more chaotic environment in which established mainstream political parties lost considerable ground to new political formations based on personalist and populist appeals? Why did this reversal in Eastern Europe happen during a period of economic recovery, remarkable Western integrati

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12

Cang, Shijian, Aiguo Wu, Ruiye Zhang, Zenghui Wang, and Zengqiang Chen. "Conservative Chaos in a Class of Nonconservative Systems: Theoretical Analysis and Numerical Demonstrations." International Journal of Bifurcation and Chaos 28, no. 07 (2018): 1850087. http://dx.doi.org/10.1142/s0218127418500876.

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This paper proposes a class of nonlinear systems and presents one example system to illustrate its interesting dynamics, including quasiperiodic motion and chaos. It is found that the example system is a subsystem of a non-Hamiltonian system, which has a continuous curve of equilibria with time-reversal symmetry. In this study, the dynamical evolution of the example system with three different kinds of external excitations are fully investigated by using general chaotic analysis methods such as Poincaré sections, phase portraits, Lyapunov exponents and bifurcation diagrams. Both theoretical an

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13

Żukowski, Witold, and Marek Berezowski. "Generation of chaotic oscillations in a system with flow reversal." Chemical Engineering Science 55, no. 2 (2000): 339–43. http://dx.doi.org/10.1016/s0009-2509(99)00329-2.

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14

Sabbah, A. S. "Level spacing distribution for a chaotic system without time reversal." Il Nuovo Cimento B 109, no. 7 (1994): 687–96. http://dx.doi.org/10.1007/bf02722526.

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15

Li, Chunbiao, Zhinan Li, Yicheng Jiang, Tengfei Lei, and Xiong Wang. "Symmetric Strange Attractors: A Review of Symmetry and Conditional Symmetry." Symmetry 15, no. 8 (2023): 1564. http://dx.doi.org/10.3390/sym15081564.

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A comprehensive review of symmetry and conditional symmetry is made from the core conception of symmetry and conditional symmetry. For a dynamical system, the structure of symmetry means its robustness against the polarity change of some of the system variables. Symmetric systems typically show symmetrical dynamics, and even when the symmetry is broken, symmetric pairs of coexisting attractors are born, annotating the symmetry in another way. The polarity balance can be recovered through combinations of the polarity reversal of system variables, and furthermore, it can also be restored by the

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16

LÜ, JINHU, GUANRONG CHEN, and DAIZHAN CHENG. "A NEW CHAOTIC SYSTEM AND BEYOND: THE GENERALIZED LORENZ-LIKE SYSTEM." International Journal of Bifurcation and Chaos 14, no. 05 (2004): 1507–37. http://dx.doi.org/10.1142/s021812740401014x.

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This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display (i) two 1-scroll chaotic attractors simultaneously, with only three equilibria, and (ii) two 2-scroll chaotic attractors simultaneously, with five equilibria. Several issues such as some basic dynamical behaviors, routes to chaos, bifurcations, periodic windows, and the compound structure of the new chaotic system are then investigated, either analytically or numerically. Of particular interest is the fact that this chaotic system can generate a complex 4-sc

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17

Bînzar, Tudor, and Cristian Lăzureanu. "On a new chaotic system." Mathematical Methods in the Applied Sciences 38, no. 8 (2014): 1631–41. http://dx.doi.org/10.1002/mma.3174.

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18

CLERC, MARCEL G., PABLO C. ENCINA, and ENRIQUE TIRAPEGUI. "SHILNIKOV BIFURCATION: STATIONARY QUASI-REVERSAL BIFURCATION." International Journal of Bifurcation and Chaos 18, no. 07 (2008): 1905–15. http://dx.doi.org/10.1142/s0218127408021440.

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A generic stationary instability that arises in quasi-reversible systems is studied. It is characterized by the confluence of three eigenvalues at the origin of complex plane with only one eigenfunction. We characterize the dynamics through the normal form that exhibits in particular, Shilnikov chaos, for which we give an analytical prediction. We construct a simple mechanical system, Shilnikov particle, which exhibits this quasi-reversal instability and displays its chaotic behavior.

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19

Mi, Bao Liang, and Guo Zeng Wu. "A New Dynamic System Analysis." Applied Mechanics and Materials 392 (September 2013): 222–26. http://dx.doi.org/10.4028/www.scientific.net/amm.392.222.

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A new four-dimensional chaotic system is presented in this paper. Some basic dynamical Properties of this chaotic system are investigated by means of Poincaré mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit implementation.

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20

Gong, Lihua, Rouqing Wu, and Nanrun Zhou. "A New 4D Chaotic System with Coexisting Hidden Chaotic Attractors." International Journal of Bifurcation and Chaos 30, no. 10 (2020): 2050142. http://dx.doi.org/10.1142/s0218127420501424.

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A new 4D chaotic system with infinitely many equilibria is proposed using a linear state feedback controller in the Sprott C system. Although the new 4D chaotic system has only two nonlinear terms, it has rich dynamic characteristics, such as hidden attractors and coexisting attractors. Besides, the freedom of offset boosting of a variable is achieved by adjusting a controlled constant. The dynamic characteristics of the new chaotic system are fully analyzed from the aspects of phase portraits, bifurcation diagrams, Lyapunov exponents and Poincaré maps. The corresponding analogue electronic ci

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21

Wang, Haijun, and Xianyi Li. "New route of chaotic behavior in a 3D chaotic system." Optik 126, no. 20 (2015): 2354–61. http://dx.doi.org/10.1016/j.ijleo.2015.05.142.

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22

Li, Shih-Yu, Cheng-Hsiung Yang, Shi-An Chen, Li-Wei Ko, and Chin-Teng Lin. "Fuzzy adaptive synchronization of time-reversed chaotic systems via a new adaptive control strategy." Information Sciences 222 (February 2013): 486–500. http://dx.doi.org/10.1016/j.ins.2012.08.007.

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23

Zhang Jian-Xiong, Tang Wan-Sheng, and Xu Yong. "A new three-dimensional chaotic system." Acta Physica Sinica 57, no. 11 (2008): 6799. http://dx.doi.org/10.7498/aps.57.6799.

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24

Ziabari, Masoud Taleb, and Ali Reza Sahab. "Control of New 3D Chaotic System." International Journal of Information Technology, Modeling and Computing 2, no. 1 (2014): 69–75. http://dx.doi.org/10.5121/ijitmc.2014.2107.

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25

Zhao, Gui Qing, and Guo Zeng Wu. "A New Chaotic Dynamic System Research." Applied Mechanics and Materials 392 (September 2013): 227–31. http://dx.doi.org/10.4028/www.scientific.net/amm.392.227.

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A new four-dimensional chaotic system is presented in this paper. Some basic dynamical Properties of this chaotic system are investigated by means of Poincaré mapping, Lyapunov exponents and bifurcation diagram. It is a new phenomenon that the phase plane attractors can achieve opposite and topology of exactly by changing the parameter symbol of c.

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26

Fa-Qiang, Wang, and Liu Chong-Xin. "A new multi-scroll chaotic system." Chinese Physics 15, no. 12 (2006): 2878–82. http://dx.doi.org/10.1088/1009-1963/15/12/019.

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27

Zhengguo Li, Kun Li, Changyun Wen, and Yeng Chai Soh. "A new chaotic secure communication system." IEEE Transactions on Communications 51, no. 8 (2003): 1306–12. http://dx.doi.org/10.1109/tcomm.2003.815058.

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28

Li, Yu Xia, Lan Ying Zhao, Wen Qing Chi, Shu Li Lu, and Xia Huang. "A New Memristor Based Chaotic System." Applied Mechanics and Materials 275-277 (January 2013): 2481–86. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.2481.

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In this paper, we present a new memristor based chaotic circuit, which is obtained by replacing the nonlinear resistor in the canonical Chua’s circuit with a charge-controlled memristor. This chaotic circuit uses only the four basic circuit elements, and has only one negative element in addition to the nonlinearity. The existence of the chaos is not only demonstrated by computer simulations, but also verified with Lyapunov exponents, bifurcation, poincaré mapping and power spectrum analysis.

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29

WANG, XINGYUAN, XIANGJUN WU, and YAHUI LANG. "A NEW CHAOTIC SYSTEM AND CONTROL." Modern Physics Letters B 21, no. 25 (2007): 1687–96. http://dx.doi.org/10.1142/s0217984907014164.

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In this paper a chaotic system is proposed via modifying hyperchaotic Chen system. Some basic dynamical properties, such as Lyapunov exponents, fractal dimension, chaotic behaviors of this system are studied. The conventional feedback, linear function feedback, nonlinear hyperbolic function feedback control methods are applied to control chaos to unstable equilibrium point. The conditions of stability to control the system is derived according to the Routh–Hurwitz criteria. Numerical results have shown the validity of the proposed schemes.

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30

Chen, Yong, and Yun-Qing Yang. "A new four-dimensional chaotic system." Chinese Physics B 19, no. 12 (2010): 120510. http://dx.doi.org/10.1088/1674-1056/19/12/120510.

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31

Qi, Guoyuan, Guanrong Chen, Shengzhi Du, Zengqiang Chen, and Zhuzhi Yuan. "Analysis of a new chaotic system." Physica A: Statistical Mechanics and its Applications 352, no. 2-4 (2005): 295–308. http://dx.doi.org/10.1016/j.physa.2004.12.040.

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32

Qi, Guoyuan, Guanrong Chen, and Yuhui Zhang. "On a new asymmetric chaotic system." Chaos, Solitons & Fractals 37, no. 2 (2008): 409–23. http://dx.doi.org/10.1016/j.chaos.2006.09.012.

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33

MasoudTaleb, Ziabari1 and Ali Reza Sahab 2. "CONTROL OF NEW 3D CHAOTIC SYSTEM." International Journal of Information Technology, Modeling and Computing (IJITMC) 2, February (2018): 01–07. https://doi.org/10.5281/zenodo.1409996.

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In this paper, a new 3D chaotic system is controlled by generalized backstepping method. Generalized backstepping method is similarity to backstepping method but generalized backstepping method is more applications in systems than it. Backstepping method is used only to strictly feedback systems but generalized backsteppingmethod expand this class. New 3D chaotic system is controlled in two participate sections; stabilization and tracking reference input. Numerical simulations are presented to demonstrate the effectiveness of the controlschemes.

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34

Al-qdah, Majdi. "A Hybrid Security System Based on Bit Rotation and Chaotic Maps." Current Signal Transduction Therapy 14, no. 2 (2019): 152–57. http://dx.doi.org/10.2174/1574362413666180813113001.

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Background: This paper presents an image security system by combining bit rotation with block based chaotic maps cryptography. Methods: The system uses permutation technique that divides the image into blocks before applying right/left rotation of bits to the pixel values based on a randomly generated key. Then, the image blocks are fused together. A scrambling operation followed by chaotic map is applied on the rotated image to diffuse the image pixels using another randomly generated key. The chaotic map scatters all the pixel positions in the image. The decryption is the complete reversal o

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35

Sambas, Aceng, Mustafa Mamat, Sundarapandian Vaidyanathan, Muhammad Mohamed, and Mada Sanjaya. "A New 4-D Chaotic System with Hidden Attractor and its Circuit Implementation." International Journal of Engineering & Technology 7, no. 3 (2018): 1245. http://dx.doi.org/10.14419/ijet.v7i3.9846.

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In the chaos literature, there is currently significant interest in the discovery of new chaotic systems with hidden chaotic attractors. A new 4-D chaotic system with only two quadratic nonlinearities is investigated in this work. First, we derive a no-equilibrium chaotic system and show that the new chaotic system exhibits hidden attractor. Properties of the new chaotic system are analyzed by means of phase portraits, Lyapunov chaos exponents, and Kaplan-Yorke dimension. Then an electronic circuit realization is shown to validate the chaotic behavior of the new 4-D chaotic system. Finally, th

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36

Hide, R. "Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo." Nonlinear Processes in Geophysics 4, no. 4 (1997): 201–5. http://dx.doi.org/10.5194/npg-4-201-1997.

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Abstract. In the interpretation of geomagnetic polarity reversals with their highly variable frequency over geological time it is necessary, as with other irregularly fluctuating geophysical phenomena, to consider the relative importance of forced contributions associated with changing boundary conditions and of free contributions characteristic of the behaviour of nonlinear systems operating under fixed boundary conditions. New evidence -albeit indirect- in favour of the likely predominance of forced contributions is provided by the discovery reported here of the possibility of complete quenc

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37

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.

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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.

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38

Sampath, Sivaperumal, Sundarapandian Vaidyanathan, Aceng Sambas, Mohamad Afendee, Mustafa Mamat, and Mada Sanjaya. "A New Four-Scroll Chaotic System with a Self-Excited Attractor and Circuit Implementation." International Journal of Engineering & Technology 7, no. 3 (2018): 1931. http://dx.doi.org/10.14419/ijet.v7i3.14865.

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This paper reports the finding a new four-scroll chaotic system with four nonlinearities. The proposed system is a new addition to existing multi-scroll chaotic systems in the literature. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. As the new four-scroll chaotic system is shown to have three unstable equilibrium points, it has a self-excited chaotic attractor. An electronic circuit simulation of the new four-scroll chaotic system is shown using MultiSIM to check the feasibility of the fou

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39

Bouteraa, Yassine, Javad Mostafaee, Mourad Kchaou, Rabeh Abbassi, Houssem Jerbi, and Saleh Mobayen. "A New Simple Chaotic System with One Nonlinear Term." Mathematics 10, no. 22 (2022): 4374. http://dx.doi.org/10.3390/math10224374.

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In this research article, a simple four-dimensional (4D) chaotic dynamic system with uncomplicated structure and only one nonlinear term is introduced. The features of the proposed design have been conducted with some standard nonlinear dynamic analysis and mathematical tools which show the chaotic nature. One of the most important indicators for detecting complexity of the chaotic systems is the Kaplan-York dimension of the system. Moreover, one of the main criteria of chaotic systems is its simplicity due to the reduction of operating costs. Therefore, it seems necessary to design a system a

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40

Cai Guo-Liang, Tan Zhen-Mei, Zhou Wei-Huai, and Tu Wen-Tao. "Dynamical analysis of a new chaotic system and its chaotic control." Acta Physica Sinica 56, no. 11 (2007): 6230. http://dx.doi.org/10.7498/aps.56.6230.

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41

Yang, Qigui, and Xinmei Qiao. "Constructing a New 3D Chaotic System with Any Number of Equilibria." International Journal of Bifurcation and Chaos 29, no. 05 (2019): 1950060. http://dx.doi.org/10.1142/s0218127419500603.

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In the chaotic polynomial Lorenz-type systems (including Lorenz, Chen, Lü and Yang systems) and Rössler system, their equilibria are unstable and the number of the hyperbolic equilibria are no more than three. This paper shows how to construct a simple analytic (nonpolynomial) chaotic system that can have any preassigned number of equilibria. A special 3D chaotic system with no equilibrium is first presented and discussed. Using a methodology of adding a constant controller to the third equation of such a chaotic system, it is shown that a chaotic system with any preassigned number of equilibr

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42

Zhao, Jiakun, Di Zhou, and Yexin Li. "A new impulsive synchronization of Chen hyper-chaotic system and Lü hyper-chaotic system." Journal of Vibration and Control 19, no. 12 (2012): 1773–78. http://dx.doi.org/10.1177/1077546312449848.

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43

Ye, Yinfang, and Jianbin He. "Constructing a New Multi-Scroll Chaotic System and Its Circuit Design." Mathematics 12, no. 13 (2024): 1931. http://dx.doi.org/10.3390/math12131931.

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Multi-scroll chaotic systems have complex dynamic behaviors, and the multi-scroll chaotic system design and analysis of their dynamic characteristics is an open research issue. This study explores a new multi-scroll chaotic system derived from an asymptotically stable linear system and designed with a uniformly bounded controller. The main contributions of this paper are given as follows: (1) The controlled system can cause chaotic behavior with an appropriate control position and parameters values, and a new multi-scroll chaotic system is proposed using a bounded sine function controller. Mea

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44

Vaidyanathan, Sundarapandian, Aceng Sambas, Sen Zhang, Mohamad Afendee Mohamed, and Mustafa Mamat. "A New Hamiltonian Chaotic System with Coexisting Chaotic Orbits and its Dynamical Analysis." International Journal of Engineering & Technology 7, no. 4 (2018): 2430. http://dx.doi.org/10.14419/ijet.v7i4.16826.

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Hamiltonian chaotic systems are conservative chaotic systems which arise in many applications in Classical Mechanics. A famous Hamiltonian chaotic system is the H´enon-Heiles system (1964), which was modeled by H´enon and Heiles, describing the nonlinear motion of a star around a galactic centre with the motion restricted to a plane. In this research work, by modifying the dynamics of the H´enon-Heiles system (1964), we obtain a new Hamiltonian chaotic system with coexisting chaotic orbits. We describe the dynamical properties of the new Hamiltonian chaotic system.

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Sambas, Aceng, Sundarapandian Vaidyanathan, Mustafa Mamat, Muhammad Afendee Mohamed, and Mada Sanjaya WS. "A New Chaotic System with a Pear-shaped Equilibrium and its Circuit Simulation." International Journal of Electrical and Computer Engineering (IJECE) 8, no. 6 (2018): 4951. http://dx.doi.org/10.11591/ijece.v8i6.pp4951-4958.

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This paper reports the finding a new chaotic system with a pear-shaped equilibrium curve and makes a valuable addition to existing chaotic systems with infinite equilibrium points in the literature. The new chaotic system has a total of five nonlinearities. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system are unveiled. An electronic circuit simulation of the new chaotic system with pear-shaped equilibrium curve is shown using Multisim to check the model feasibility.

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Zhou, Ziwei, and Shuo Wang. "Design and implementation of a new fractional-order Hopfield neural network system." Physica Scripta 97, no. 2 (2022): 025206. http://dx.doi.org/10.1088/1402-4896/ac4c50.

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Abstract In this work, a novel chaotic system of fractional-order based on the model of Hopfield Neural Network (HNN) is proposed. The numerical solutions of the 4-neurons-based HNN fractional-order chaotic system are obtained by using the Adomain decomposition method. The dynamical performances of the 4-neurons-based HNN fractional-order chaotic system are explored through attractor trajectories, bifurcation diagrams, Lyapunov exponents, SE complexity and chaotic diagram based on SE complexity. In addition, the 4-neurons-based HNN fractional-order chaotic system is implemented based on the Mu

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Jiang, Cuimei, Shutang Liu, and Chao Luo. "A New Fractional-Order Chaotic Complex System and Its Antisynchronization." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/326354.

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We propose a new fractional-order chaotic complex system and study its dynamical properties including symmetry, equilibria and their stability, and chaotic attractors. Chaotic behavior is verified with phase portraits, bifurcation diagrams, the histories, and the largest Lyapunov exponents. And we find that chaos exists in this system with orders less than 5 by numerical simulation. Additionally, antisynchronization of different fractional-order chaotic complex systems is considered based on the stability theory of fractional-order systems. This new system and the fractional-order complex Lore

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Jiangang, Zhang, Chu Yandong, Du Wenju, Chang Yingxiang, and An Xinlei. "Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement Function." Journal of Applied Mathematics 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/371509.

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A new approach to generate chaotic phenomenon, called chaos entanglement, is introduced in this paper. The basic principle is to entangle two or multiple stable linear subsystems by entanglement functions to form an artificial chaotic system such that each of them evolves in a chaotic manner. The Hopf bifurcation of a new chaotic system with chaos entanglement function is studied. More precisely, we study the stability and bifurcations of equilibrium in the new chaotic system. Besides, we controlled the system to any fixed point to eliminate the chaotic vibration by means of sliding mode metho

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Lu, Xiaoting, Yongjian Liu, Aimin Liu, and Chunsheng Feng. "New geometric viewpoints to Chen chaotic system." Miskolc Mathematical Notes 23, no. 1 (2022): 339. http://dx.doi.org/10.18514/mmn.2022.3787.

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Zhao, Huitao, Yiping Lin, and Yunxian Dai. "A New Feigenbaum-Like Chaotic 3D System." Discrete Dynamics in Nature and Society 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/328143.

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Based on Sprott N system, a new three-dimensional autonomous system is reported. It is demonstrated to be chaotic in the sense of having positive largest Lyapunov exponent and fractional dimension. To further understand the complex dynamics of the system, some basic properties such as Lyapunov exponents, bifurcation diagram, Poincaré mapping, and period-doubling route to chaos are analyzed with careful numerical simulations. The obtained results also show that the period-doubling sequence of bifurcations leads to a Feigenbaum-like strange attractor.

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