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On the analysis of local bifurcation and topological horseshoe of a new 4D hyper-chaotic system

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  • Zhou, Leilei
  • Chen, Zengqiang
  • Wang, Zhonglin
  • Wang, Jiezhi

Abstract

In this paper, a new four-dimensional (4D) smooth quadratic autonomous system with complex hyper-chaotic dynamics is presented and analyzed. The Lyapunov exponent (LE) spectrum, bifurcation diagram and various phase portraits of the system are provided. The stability, Hopf bifurcation and pitchfork bifurcation of equilibrium point are discussed by using the center manifold theorem and bifurcation theory. Numerical simulation results are consistent with the theoretical analysis. Besides, by combining the topological horseshoe theory with a computer-assisted method of Poincaré maps and utilizing the algorithm for finding horseshoes in 3D hyper-chaotic maps, a horseshoe with two-directional expansions in the 4D hyper-chaotic system is successfully found, which rigorously proves the existence of hyper-chaos in theory.

Suggested Citation

  • Zhou, Leilei & Chen, Zengqiang & Wang, Zhonglin & Wang, Jiezhi, 2016. "On the analysis of local bifurcation and topological horseshoe of a new 4D hyper-chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 148-156.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:148-156
    DOI: 10.1016/j.chaos.2016.05.017
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    References listed on IDEAS

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    1. Qingdu Li & Xiao-Song Yang, 2007. "A 3D Smale Horseshoe in a Hyperchaotic Discrete-Time System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2007, pages 1-9, January.
    2. Qi, Guoyuan & Chen, Guanrong & Du, Shengzhi & Chen, Zengqiang & Yuan, Zhuzhi, 2005. "Analysis of a new chaotic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 295-308.
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    Cited by:

    1. Ren, Hai-Peng & Tian, Kun & Grebogi, Celso, 2020. "Topological horseshoe in a single-scroll Chen system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. Maximenko, Vladimir A. & Hramov, Alexander E. & Koronovskii, Alexey A. & Makarov, Vladimir V. & Postnov, Dmitry E. & Balanov, Alexander G., 2017. "Lyapunov analysis of the spatially discrete-continuous system dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 228-237.

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