Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center
The objective of this paper is the upper bound for the maximum number of limit cycles that a planar discontinuous piecewise linear differential systems with two pieces separated by a straight line can have, when there is no a singularity of the two linear differential systems on the discontinuity straight line. The main result is formulated as follows: if one of the two linear differential systems has a center, real or virtual, then the discontinuous piecewise linear differential system has at most two limit cycles. More precisely, two limit cycles can appear only in the case that the focus is real. To prove it the authors use the canonical forms of all the possible configurations of the discontinuous piecewise linear differential systems in \(\mathbb{R}^2\) with two pieces separated by a straight line when both systems have a singularity.
discontinuous piecewise linear differential system
scientific article; zbMATH DE number 6918465
scientific article