**Xinhe Zhu <sup>1</sup> and Wei-Shih Du 2,\***


Received: 2 June 2019; Accepted: 16 July 2019; Published: 26 July 2019

**Abstract:** 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.

**Keywords:** chaos; bifurcation; closed curve equilibrium; synchronization
