Maximum Number of Limit Cycles for Certain Piecewise Linear Dynamical Systems
نویسندگان
چکیده
In this paper we compute the maximum number of limit cycles of some classes of planar discontinuous piecewise linear differential systems defined in two half–planes separated by a straight line Σ. Here we only consider non–sliding limit cycles, i.e. the limit cycle does not contain any sliding segment. Among all the cases that we study, in particular, we prove that this maximum number of limit cycles is 2, 1 or 1 if one of the two linear differential systems of the discontinuous piecewise linear differential system is a focus in Σ, a center, or a weak saddle, respectively. We also provide some normal forms for these systems.
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