New Chaotic Systems with Two Closed Curve Equilibrium Passing the Same Point: Chaotic Behavior, Bifurcations, and Synchronization

Symmetry

Wei-Shih Du¹  Xinhe Zhu² 

[1] Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan;School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China;

关键词: chaos;    bifurcation;    closed curve equilibrium;    synchronization;   

DOI  :  10.3390/sym11080951

来源: DOAJ

【 摘 要 】

In this work, we introduce a chaotic system with infinitely many equilibrium points laying on two closed curves passing the same point. The proposed system belongs to a class of systems with hidden attractors. The dynamical properties of the new system were investigated by means of phase portraits, equilibrium points, Poincaré section, bifurcation diagram, Kaplan−Yorke dimension, and Maximal Lyapunov exponents. The anti-synchronization of systems was obtained using the active control. This study broadens the current knowledge of systems with infinite equilibria.

【 授权许可】

Unknown