Arbitrary number of limit cycles for planar discontinuous piecewise linear differential systems with two zones

Abstract

For any given positive integer $n$ we show the existence of a class of discontinuous piecewise linear differential systems with two zones in the plane having exactly $n$ hyperbolic limit cycles. Moreover, all the points on the separation boundary between the two zones are of sewing type, except the origin which is the only equilibrium point.

Keywords

• Piecewise linear differential system
• limit cycle
• non-smooth differential system