On the Limit Cycles for a Class of Continuous Piecewise Linear Differential Systems with Three Zones

Abstract

In this paper we consider a class of planar continuous piecewise linear vector fields with three zones. Using the Poincaré map we show that these systems admit always a unique limit cycle, which is hyperbolic.

Limit Cycles in Planar Piecewise Linear Hamiltonian Systems with Three Zones Without Equilibrium Points

“…In fact, as far as we know, the studies found in the pertinent literature deal with piecewise smooth systems with three zones in the plane with at least one equilibrium point which can be real or virtual. This is the case, for instance, in the studies carried out in [3], [6], [7], [8], [9], [10]. We emphasize that in these articles the authors studied the existence and the number of limit cycles under the hypothesis of the continuity of the vector fields in the separation curves which are straight lines.…”