Abstract
AbstractThis paper includes some new results and a survey of known bifurcations for a family of Filippov systems. Such a family is constituted by planar piecewise linear systems with a discontinuity line where the crossing set is maximal and it has two dynamics of focus type. From the natural 12 parameters needed we obtain, under some generic conditions, a Liénard canonical form topologically equivalent to the original system with only four parameters. We describe, taking into account the number of equilibria inside each zone of linearity: zero, one or two, the qualitatively different phase portraits that can occur and the bifurcations connecting them.KeywordsPeriodic OrbitEquilibrium PointHopf BifurcationCanonical FormBoundary EquilibriumThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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