Journal of Guangxi Normal University(Natural Science Edition) ›› 2021, Vol. 39 ›› Issue (5): 173-181.doi: 10.16088/j.issn.1001-6600.2020121402

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Research on Complex Dynamics of a New Four-dimensional Hyperchaotic System with Finite and Infinite Isolated Singularities

RUAN Wenjing, YANG Qigui*   

  1. School of Mathematics, South China University of Technology, Guangzhou Guangdong 510640, China
  • Received:2020-12-14 Revised:2021-02-03 Online:2021-09-25 Published:2021-10-19

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Abstract: Based on the Sprott A chaotic system, by designing a feedback controller, this paper proposes a new four-dimensional autonomous hyperchaotic system with an infinite number of isolated singularities and only two symmetrical singularities. The stability of the non-hyperbolic singularities of this type of new system is discussed by using the central manifold theory, and the Hopf bifurcation is strictly proved. Furthermore, by using numerical methods such as Lyapunov exponential spectrum, bifurcation graph and Poincaré mapping, the existence of periodic attractors, chaotic attractors and hyperchaotic attractors of the new system is obtained.

Key words: hyperchaos, attractor, Hopf bifurcation, complex dynamics, stability

CLC Number: 

  • O415.5
[1] LORENZ E N. Deterministic non-periodic flow[J]. Journal of the Atmospheric Sciences, 1963, 20(2): 130-141.
[2] RÖSSLER O E. An equation for hyperchaos[J]. Physics Letters A, 1979, 71(2/3): 155-157.
[3] MATSUMOTO T, CHUA L O, KOBAYASHI K. Hyperchaos: Laboralory experiment and numerical confirmation[J]. IEEE Transaction on Circuits and Systems, 1986, 33(11): 1143-1147.
[4] SU Q, WANG C, CHEN H, et al. A new method for generating chaotic system with arbitrary shaped distributed attractors[J]. Chaos, 2018, 28(7): 073106.
[5] 张锦炎, 冯贝叶.常微分方几何理论与分支问题[M].北京: 北京大学出版社,2000: 329-378.
[6] 张芷芬, 丁同仁,黄文灶,等. 微分方程定性理论[M]. 北京: 科学出版社, 1997: 435-436.
[7] YANG T, YANG Q G. A 3D autonomous system with infinitely many chaotic attractors[J]. International Journal of Bifurcation and Chaos, 2019, 29(12): 1950166.
[8] YANG Q G, ZHANG K M, CHEN G R. Hyperchaotic attractors from a linearly controlled Lorenz system[J]. Nonlinear Analysis: Real World Applications, 2008, 10(3): 1601-1617.
[9] CHEN Y M, YANG Q G. Dynamics of a hyperchaotic Lorenz-type system[J]. Nonlinear Dynamic, 2014, 77: 569-581.
[10] YANG Q G, LIU Y J. A hyperchaotic system from a chaotic system with one saddle and two stable node-foci[J]. Journal of Mathematical Analysis and Applications, 2009, 360(1): 293-306.
[11] CHEN Y M, YANG Q G. A new Lorenz-type hyperchaotic system with a curve of equilibria[J]. Mathematics and Computers in Simulation, 2015, 112: 40-55.
[12] 张艳红.具有无穷多孤立奇点或无奇点的新四维超混沌系统的动力学研究[D].广州:华南理工大学, 2017.
[13] SPROTT J C. Some simple chaotic flows[J]. Physical Review E, 1994, 50(2): 647-650.
[14] YANG Q G, QIAO X M. Constructing a new 3D chaotic system with any number of equilibria[J]. Internatioanal Journal of Bifurcation and Chaos, 2019, 29(5): 1950060.
[15] WIGGINS S. Introduction to applied nonlinear dynamical system and chaos[M]. New York: Springer, 2003: 608-615.
[16] HASSARD B, KAZARINOFF N, WAN Y. Theory and application of Hopf bifurcation[M]. Cambridge: Cambridge University Press, 1981: 14-70.
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