On the bifurcation of periodic orbits in discontinuous systems (Q969208)

Bifurcation scenarios of periodic orbits in discontinuous systems are discussed; such systems are given by differential equations with discontinuity boundaries which divide the phase space into two (or more) parts. The authors first use a Poincaré function and a method of Melnikov type to give a sufficient condition for the persistence of a piecewise \(C^1\)-orbit. Sufficient conditions for bifurcations in planar discontinuous systems (a piecewise nonlinear and linear equation) are discussed in the last part of the paper.