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

Haijun Wang (), Guiyao Ke (), Jun Pan (), Feiyu Hu (), Hongdan Fan () and Qifang Su ()
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Haijun Wang: Taizhou University
Guiyao Ke: Zhejiang Guangsha Vocational and Technical University of Construction
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

The European Physical Journal B: Condensed Matter and Complex Systems, 2023, vol. 96, issue 3, 1-9

Abstract: 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

Date: 2023
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DOI: 10.1140/epjb/s10051-023-00491-5

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