Dynamics, Circuit Design, and Synchronization of a New Chaotic System with Closed Curve Equilibrium

Abstract

After the report of chaotic flows with line equilibrium, there has been much attention to systems with uncountable equilibria in the past five years. This work proposes a new system with an infinite number of equilibrium points located on a closed curve. It is worth noting that the new system generates chaotic behavior as well as hidden attractors. Dynamics of the system with closed curve equilibrium have been investigated by using phase portraits, bifurcation diagram, maximal Lyapunov exponents, and Kaplan–York dimension. In addition, we introduce an electronic implementation of the theoretical system to verify its feasibility. Antisynchronization ability of the new system with infinite equilibria is studied by applying an adaptive control. This study suggests that there exist other chaotic systems with uncountable equilibria in need of further investigation.