https://doi.org/10.1140/epjb/s10051-023-00491-5
Regular Article - Statistical and Nonlinear Physics
Two pairs of heteroclinic orbits coined in a new sub-quadratic Lorenz-like system
1
School of Electronic and Information Engineering (School of Big Data Science), Taizhou University, 318000, Taizhou, People’s Republic of China
2
School of Information, Zhejiang Guangsha Vocational and Technical University of Construction, 322100, Dongyang, Zhejiang, People’s Republic of China
3
School of Information Engineering, GongQing Institute of Science and Technology, 332020, Gongqingcheng, People’s Republic of China
4
Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, 310023, Hangzhou, People’s Republic of China
5
College of Sustainability and Tourism Ritsumeikan Asia Pacific University, Jumonjibaru, 874-8577, Beppu, Oita, Japan
Received:
5
June
2022
Accepted:
6
February
2023
Published online:
5
March
2023
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 
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