Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center

By Jaume Llibre, Xiang Zhang. Journal of Mathematical Analysis and Applications, 2018

53 citations recorded by the source corpus.

Abstract From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles that this class of differential systems can have? Here we prove that when one of the linear differential systems has a center, real or virtual, then the discontinuous piecewise linear differential system has at most two limit cycles.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/495145e1548ee8e679ef30a32a829e006fffff3e