Simplest Chaotic Flows with Involutional Symmetries

Abstract

A chaotic flow has an involutional symmetry if the form of the dynamical equations remains unchanged when one or more of the variables changes sign. Such systems are of theoretical and practical importance because they can exhibit symmetry breaking in which a symmetric pair of attractors coexist and merge into one symmetric attractor through an attractor-merging bifurcation. This paper describes the simplest chaotic examples of such systems in three dimensions, including several cases not previously known, and illustrates the attractor-merging process.