A topological computation approach to the interior crisis bifurcation

Abstract

We study the interior crisis bifurcation from the viewpoint of the graph-based topological computation developed in [2]. We give a new formulation of the interior crisis bifurcation in terms of a change of the attractor-repeller decompositions of the dynamics, and prove that the attractor before the crisis disappears by creating a chain connecting orbit to the repeller at the moment of the interior crisis. As an illustration, we discuss the interior crisis bifurcation in the Ikeda map.