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Limit cycle bifurcations in discontinuous planar systems with multiple lines
Yanqin Xiong,Maoan Han
Keywords:Discontinuous planar system, limit cycle, bifurcation, periodic orbit, Melnikov function.
Abstract:
      In this paper, the limit cycle bifurcation problem is investigated for a class of planar discontinuous perturbed systems with $n$ parallel switch lines. Under the restriction that the unperturbed system has a family of periodic orbits crossing all of the lines, an explicit expression of the first order Melnikov function along the periodic orbits is presented, which plays an important role in studying the problem of Poincar\'{e}, Hopf and Homoclinic bifurcations. As an application to the established method, the maximal number of limit cycles for a discontinuous system is considered.