Piecewise linear differential systems with two real saddles

Three Limit Cycles in Discontinuous Piecewise Linear Differential Systems with Two Zones

In this paper we study a planar piecewise linear differential system formed by two regions separated by a straight line so that one system has a real unstable focus and the other a virtual stable focus which coincides with the real one. This system was introduced by S.-M. Huan and X.-S. Yang in [8] who numerically showed that it can exhibit 3 limit cycles surrounding the real focus. This is the...

Three Nested Limit Cycles in Discontinuous Piecewise Linear Differential Systems with Two Zones

In this paper we study a planar piecewise linear differential system formed by two regions separated by a straight line so that one system has a real unstable focus and the other a virtual stable focus which coincides with the real one. This system was introduced in a very recent paper (On the number of limit cycles in general planar piecewise linear systems, Discrete and Continuous Dynamical S...

Topological dynamics of generic piecewise continuous contractive maps in n dimensions

We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the “separation property”: different continuity pieces have disjoint images. The continuity pieces act as stable topological manifolds while the points in the discontinuity lines, separating different conti...

Piecewise Constant Controlled Linear Fuzzy Systems

On the Number of Limit Cycles in Discontinuous Piecewise Linear Differential Systems with Two Pieces Separated by a Straight Line

In this paper we study the maximum number N of limit cycles that can exhibit a planar piecewise linear differential system formed by two pieces separated by a straight line. More precisely, we prove that this maximum number satisfies 2 ≤ N ≤ 4 if one of the two linear differential systems has its equilibrium point on the straight line of discontinuity.