Border collision bifurcations and chaotic sets in a two-dimensional piecewise linear map

Abstract

A two-dimensional piecewise linear continuous model is analyzed. It reflects the dynamics occurring in a circuit proposed as chaos generator, in a simplified case. The parameter space is investigated in order to classify completely regions of existence of stable cycles, and regions associated with chaotic behaviors. The border collision bifurcation curves are analytically detected, as well as the degenerate flip bifurcations of k-cycles and the homoclinic bifurcations occurring in cyclic chaotic regions leading to chaos in one-piece.