Multistable dynamics and attractors self-reproducing in a new hyperchaotic complex Lü system

Yujuan Gu; Guodong Li; Xiangliang Xu; Xiaoming Song; Si Wu

doi:10.1063/5.0158163

Multistable dynamics and attractors self-reproducing in a new hyperchaotic complex Lü system

Chaos. 2023 Sep 1;33(9):093112. doi: 10.1063/5.0158163.

Authors

Yujuan Gu¹, Guodong Li^{1

2}, Xiangliang Xu^{1

3}, Xiaoming Song¹, Si Wu¹

Affiliations

¹ School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China.
² Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Center for Applied Mathematics of Guangxi (GUET), Guilin University of Electronic Technology, Guilin 541004, China.
³ School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China.

PMID: 37695926
DOI: 10.1063/5.0158163

Abstract

Multistable dynamics analysis of complex chaotic systems is an important problem in the field of chaotic communication security. In this paper, a new hyperchaotic complex Lü system is proposed and its basic dynamics are analyzed. Owing to the introduction of complex variables, the new system has some structurally distinctive attractors, such as flower-shaped and airfoil-shaped attractors. In addition, the evolution process of the limit cycle is also investigated. Next, the multistable coexistence behavior of the system is researched by the method of attraction basins, and the coexistence behavior of two types of hyperchaotic attractors and one type of chaotic and periodic attractors of the system are analyzed. The coexisting hyperchaotic attractors also show flower and airfoil shapes, and four types of coexistence flower-shaped attractors with different structures are perfectly explored. Moreover, the variation of coexistence attractors in the plane and space with parameters is discussed. Then, by introducing a specific piecewise function determined by a two-element method into the new high-dimensional system, the self-reproduction of the attractor can be realized to generate the multistability, and the general steps of attractors self-reproducing in the higher dimensional system are given. Finally, the circuit design of the new system is implemented, which lays a foundation for the application of complex chaotic systems.