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

Zeraoulia Elhadj
Department of Mathematics, University of Tébessa, (12002), Algeria.
e-mail: [email protected], and [email protected].

J. C. Sprott
Department of Physics, University of Wisconsin, Madison, WI 53706, USA.
e-mail: [email protected].

Abstract

In this paper we introduce a new piecewise smooth mapping of the plane as a unified discrete-time chaotic system that contains the original H´enon 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.

Manuscript accepted November 12, 2011.

Ref: E. Zeraoulia and J. C. Sprott, Annual Review of Chaos Theory, Bifurcations and Dynamical Systems 1, 50-60 (2012)

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