Dynamical Phenomena Based on Chaotic Systems Without Equilibria

• Published in: International journal of bifurcation and chaos in applied sciences and engineering Vol. 34; no. 14
• Main Authors: Zhao, Boyu, Ye, Xiaolin
• Format: Journal Article
• Language: English
• Published: Singapore World Scientific Publishing Company 01.11.2024; World Scientific Publishing Co. Pte., Ltd
• Subjects: Chaos theory; Dynamic characteristics; Equilibrium; Rotation; Trigonometric functions; hidden attractor; No equilibrium point; coexisting attractor
• ISSN: 0218-1274; 1793-6551
• DOI: 10.1142/S0218127424501785

A chaotic system without equilibrium points is a focal subject in recent years, and its unique dynamic characteristics have attracted extensive research. In this paper, different chaotic systems with no equilibrium points are constructed by modifying the Sprott-A system. The test results show that the first system is conservative. After investigating the hidden dynamical behavior of the first system, the rotation attractor phenomenon is revealed by the rotation factor. Next, we make a second transformation of the Sprott-A system. By introducing a trigonometric function, we get a new system that can generate infinitely many coexisting grid attractors. After calculation, we find that the new system still belongs to the chaotic system without equilibrium points and the coexistence phenomenon of attractors is created by adjusting the initial value continuously. The chaotic system without equilibrium points which can realize the coexistence of attractors has potential applications in some related fields, which is worthy of further study.