A chaotic system with Hölder continuity

Abstract

This paper presents a new chaotic system with infinitely many equilibria. The new system contains two system parameters and a nonlinear term which does not satisfy Lipschitz continuity but does satisfy 1 2 -Hölder continuity condition. The complicated dynamics are studied through theoretical analysis and numerical simulation. Synchronization for two identical systems by a piecewise linear feedback controller is investigated based on Lyapunov stability criteria.

A novel bounded 4D chaotic system

“…Xu and Yu [14] presented some multi-scroll chaotic attractors generated using hyperbolic functions. More recently, a novel chaotic system with infinitely many equilibria was proposed in [15], in which the nonlinear term does not satisfy Lipschitz continuity condition. Up to now, chaos generation has attracted the sustained attention of researchers.…”

“…It is noted that most of the research in this area has focused on the family of Lorenz chaotic systems. In fact, many chaotic systems are shown to not have a globally attractive set such as those presented in [9][10][11][12][13][14][15]. For the systems proposed in [5,6,8], it is very hard to construct analytically the set by the Lyapunov functions technique even though there may be a globally attractive set shown from numerical simulation.…”