New class of chaotic systems with equilibrium points like a three-leaved clover

Abstract

This paper presents a new class of chaotic systems with infinite number of equilibrium points like a three-leaved clover. They signify an exciting class of dynamical systems which represent many major characteristics of regular and chaotic motions. These chaotic systems belong to the general class of chaotic systems with hidden attractors. By using a systematic computer search, three chaotic systems with three-leaved-clover-shaped equilibria were found which are classified into dissipative systems. Dynamics of the chaotic system with the three-leaved-clover-equilibria has been investigated by using phase portraits, bifurcation diagram, Lyapunov exponents, Kaplan–Yorke dimension and Poincare map. Moreover, an electronic circuit implementation of the theoretical system is designed to check its effectiveness. Random number generator design has been realized with newly developed chaotic systems. The obtained random bit sequences are used for image encryption. Security analysis of image encryption processes has been performed.