Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous Systems
arXiv:1006.4123 · doi:10.1016/j.physd.2011.05.002
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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- Dimension reduction for slow-fast, piecewise-smooth, continuous systems of ODEs
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