[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2012.52.4.459

Dangerous Border-collision Bifurcation for a Piecewise Smooth Nonlinear System

Kang, Hunseok (Department of Mathematics, Soongsil University)

Publication Information

Kyungpook Mathematical Journal / v.52, no.4, 2012 , pp. 459-472 More about this Journal

Abstract

A piecewise smooth system is characterized by non-differentiability on a curve in the phase space. In this paper, we discuss particular bifurcation phenomena in the dynamics of a piecewise smooth system. We consider a two-dimensional piecewise smooth system which is composed of a linear map and a nonlinear map, and analyze the stability of the system to determine the existence of dangerous border-collision bifurcation. We finally present some numerical examples of the bifurcation phenomena in the system.

Keywords

piecewise smooth system; (dangerous) border-collision bifurcation;

Citations & Related Records

Reference

1	Y. Do, A mechanism for dangerous border collision bifurcations, Chaos Soliton Fractal, 32(2007), 352-362. DOI ScienceOn
2	Y. Do, S. Kim and P. Kim, Stability of fixed points placed on the border in the piecewise linear systems, Chaos Soliton Fractal, 38(2008), 391-399. DOI ScienceOn
3	A. Ganguli and S. Banerjee, Dangerous bifurcation at border collision: When does it occur?, Phys. Rev. E, 59(2005), 5253.
4	M. Hassouneh, E. Abed, H. Nusse, Robust dangerous border-collision bifurcation in piecewise smooth systems, Phys. Rev. Lett., 92(2004), 070201. DOI ScienceOn
5	H. Nusse and J. Yorke, Border-collision bifurcation including "period two to period three" for piecewise smooth systems, Phys. D, 57(1992), 39-57. DOI ScienceOn
6	H. Nusse, E. Ott and J. Yorke, Border-collision bifurcations: An explanation for observed bifurcation phenomena, Phys. Rev. E., 49 (1994), 1073-1076. DOI ScienceOn
7	G. Yuan, S. Banerjee, E. Ott and J. Yorke, Border-collision bifurcations in the buck converter, IEEE Trans. Circ. Syst., 45(1998), 707-716. DOI ScienceOn
8	Z. Zhusubaliyev and E. Mosekilde, Bifurcations And Chaos In Piecewise-Smooth Dynamical Systems, World Scientific Series on Nonlinear Science Series A, 44(2003).