Bifurcations in Nonsmooth Dynamical Systems

@article{Bernardo2008BifurcationsIN,
  title={Bifurcations in Nonsmooth Dynamical Systems},
  author={Mario di Bernardo and Chris J. Budd and Alan R. Champneys and Piotr Kowalczyk and Arne B. Nordmark and Gerard Olivar and Petri T. Piiroinen},
  journal={SIAM Review},
  year={2008},
  volume={50},
  pages={629-701}
}
A review is presented of the one-parameter, nonsmooth bifurcations that occur in a variety of continuous-time piecewise-smooth dynamical systems. Motivated by applications, a pragmatic approach is taken to defining a discontinuity-induced bifurcation (DIB) as a nontrivial interaction of a limit set with respect to a codimension-one discontinuity boundary in phase space. Only DIBs that are local are considered, that is, bifurcations involving equilibria or a single point of boundary interaction… CONTINUE READING
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