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September  2006, 5(3): 493-503. doi: 10.3934/cpaa.2006.5.493

Dangerous Border-Collision bifurcations of a piecewise-smooth map

Hun Ki Baek 1, and  Younghae Do 1,

1. 

Department of Mathematics, Kyungpook National University, Daegu, 702-701, South Korea, South Korea

Received  June 2005 Revised  February 2006 Published  June 2006

In this paper we study the dangerous border-collision bifurcations [8] which recently have been numerically found on piecewise smooth maps characterized by non-differentiability on some surface in the phase space. The striking feature of such bifurcations is characterized by exhibiting a stable fixed point before and after the critical bifurcation point, but the unbounded behavior of orbits at the critical bifurcation point. We consider a specific variable space in order to do an analytical investigation of such bifurcations and prove the stability of fixed points. We also extend these bifurcation phenomena for the fixed points to the multiple coexisting attractors.
Keywords: chaos., border-collision bifurcation, Fixed points, nonsmooth.
Mathematics Subject Classification: 37C05, 37C37, 37G35, 37H2.
Citation: Hun Ki Baek, Younghae Do. Dangerous Border-Collision bifurcations of a piecewise-smooth map. Communications on Pure and Applied Analysis, 2006, 5 (3) : 493-503. doi: 10.3934/cpaa.2006.5.493
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