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A novel hyperchaotic system with infinitely many heteroclinic orbits coined

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  • Wang, Haijun
  • Li, Xianyi

Abstract

Based on the famous Shimizu–Morioka system, this paper proposes a novel five-dimensional Shimizu–Morioka-type hyperchaotic system that has an infinite set of heteroclinic orbits. Of particular interest are the following observed properties of the system: (i) the existence of both ellipse-parabola-type and hyperbola-parabola-type of equilibria; (ii) the strange attractor coexisting either non-isolated equilibria or two pairs of symmetrical equilibria; (iii) the existence of the proposed strange attractors and hyperchaotic attractors bifurcated from the corresponding singularly degenerate heteroclinic cycles; (iv) the existence of an infinite set of both ellipse-parabola-type and hyperbola-parabola-type heteroclinic orbits.

Suggested Citation

  • Wang, Haijun & Li, Xianyi, 2018. "A novel hyperchaotic system with infinitely many heteroclinic orbits coined," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 5-15.
    • Handle: RePEc:eee:chsofr:v:106:y:2018:i:c:p:5-15
    DOI: 10.1016/j.chaos.2017.10.029
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    References listed on IDEAS

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    1. Pan, Indranil & Das, Saptarshi, 2015. "When Darwin meets Lorenz: Evolving new chaotic attractors through genetic programming," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 141-155.
    2. Chen, Yuming & Yang, Qigui, 2015. "A new Lorenz-type hyperchaotic system with a curve of equilibria," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 112(C), pages 40-55.
    3. LeBaron, Blake & Arthur, W. Brian & Palmer, Richard, 1999. "Time series properties of an artificial stock market," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1487-1516, September.
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    Cited by:

    1. Haijun Wang & Guiyao Ke & Jun Pan & Feiyu Hu & Hongdan Fan & Qifang Su, 2023. "Two pairs of heteroclinic orbits coined in a new sub-quadratic Lorenz-like system," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(3), pages 1-9, March.
    2. Wang, Haijun & Dong, Guili, 2019. "New dynamics coined in a 4-D quadratic autonomous hyper-chaotic system," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 272-286.

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