Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special section on Recent Progress in Verified Numerical Computations
A topological computation approach to the interior crisis bifurcation
Hiroshi KokubuHiroe Oka
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2013 Volume 4 Issue 1 Pages 97-103

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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.

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© 2013 The Institute of Electronics, Information and Communication Engineers
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