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Two pairs of heteroclinic orbits coined in a new sub-quadratic Lorenz-like system

Author

Listed:
  • Haijun Wang

    (Taizhou University)

  • Guiyao Ke

    (Zhejiang Guangsha Vocational and Technical University of Construction
    GongQing Institute of Science and Technology)

  • Jun Pan

    (Zhejiang University of Science and Technology)

  • Feiyu Hu

    (College of Sustainability and Tourism Ritsumeikan Asia Pacific University, Jumonjibaru)

  • Hongdan Fan

    (Zhejiang University of Science and Technology)

  • Qifang Su

    (Taizhou University)

Abstract

This paper reports a new 3D sub-quadratic Lorenz-like system and proves the existence of two pairs of heteroclinic orbits to two pairs of nontrivial equilibria and the origin, which are completely different from the existing ones to the unstable origin and a pair of stable nontrivial equilibria in the published literature. This motivates one to further explore it and dig out its other hidden dynamics: Hopf bifurcation, invariant algebraic surface, ultimate boundedness, singularly degenerate heteroclinic cycle and so on. Particularly, numerical simulation illustrates that the Lorenz-like chaotic attractors coexist with one saddle in the origin and two stable nontrivial equilibria, which are created through the broken infinitely many singularly degenerate heteroclinic cycles and explosions of normally hyperbolic stable foci $$E_{z}.$$ E z . Graphical abstract

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurphb:v:96:y:2023:i:3:d:10.1140_epjb_s10051-023-00491-5
    DOI: 10.1140/epjb/s10051-023-00491-5
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. N. C. Pati, 2023. "Bifurcations and multistability in a physically extended Lorenz system for rotating convection," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(8), pages 1-15, August.

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