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arXiv · 1006.4123

Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous Systems

D. J. W. Simpson·J. D. Meiss
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Abstract

Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a surface on which the system is not smooth. Much of our understanding of these cases relies on a reduction to piecewise linearity near the border-collision. We also review a number of codimension-two bifurcations in which nonlinearity is important.

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BibTeXRIS

D. J. W. Simpson, J. D. Meiss. 2010-06-21. Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous Systems. https://doi.org/10.1016/j.physd.2011.05.002

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