A Unified Piecewise Smooth Chaotic Mapping that Contains the Hénon and the Lozi Systems

In this paper we introduce a new piecewise smooth mapping of the plane as a unified discrete-time chaotic system that contains the original Hénon and Lozi systems as two extremes and other systems as a transition in between and that has robust homoclinic chaos over a portion of its key system parameters. Dynamical behaviors of the unified system are investigated in some detail.