https://doi.org/10.1140/epjs/s11734-021-00423-3
Regular Article
Multitudinous potential hidden Lorenz-like attractors coined
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 Engineering, GongQing Institute of Science and Technology, 332020, Gongqingcheng, People’s Republic of China
3
Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, 310023, Hangzhou, People’s Republic of China
4
Institute of Nonlinear Analysis and Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou, 310023, People’s Republic of China
Received:
23
June
2021
Accepted:
16
December
2021
Published online:
4
January
2022
Very little research is available in the field of sub-quadratic chaotic systems. This note reports a new 3D sub-quadratic Lorenz-like system: 
, 
, 
. Except for the rich dynamics, i.e., generic and degenerate pitchfork bifurcation, first integral, invariant algebraic surface, ultimate bounded set, singularly degenerate heteroclinic cycle with nearby chaotic attractor, and existence of a pair of heteroclinic orbits, etc., this proposed system gives birth to Lorenz-like chaotic attractors coexisting the unstable origin and two stable node-foci in a broad range of the parameter c and thus hidden attractors are coined, which verifies the guess that the decrease of powers of some variable states may widen the ranges of some parameters for which hidden attractors exist. This may not only provide a new method to detect hidden Lorenz-like attractors, but also pose an interesting problem that the existence of hidden attractors can be determined by the degrees of the variables of the studied systems.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2022
