Crossing Limit Cycles of Planar Piecewise Linear Hamiltonian Systems without Equilibrium Points

On the Existence and Uniqueness of Limit Cycles in Planar Piecewise Linear Systems without Symmetry

Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewise-linear differential systems. New results are obtained for systems with three linearity zones without symmetry and having one equilibrium point in the central region. We also revisit the case of systems with only two linear zones giving shorter pro...

Arbitrary Number of Limit Cycles for Planar Discontinuous Piecewise Linear Differential Systems with Two Zones

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.

Regions of Stability for Limit Cycles of Piecewise Linear Systems

This paper starts by presenting local stability conditions for limit cycles of piecewise linear systems (PLS), based on analyzing the linear part of Poincaré maps. Local stability guarantees the existence of an asymptotically stable neighborhood around the limit cycle. However, tools to characterize such neighborhood do not exist. This work gives conditions in the form of LMIs that guarantee as...

Limit cycles of Discontinuous Piecewise Linear differential Systems

We study the bifurcation of limit cycles from the periodic orbits of a 2−dimensional (respectively 4−dimensional) linear center in R perturbed inside a class of discontinuous piecewise linear differential systems. Our main result shows that at most 1 (respectively 3) limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This uppe...

Planar Bimodal Piecewise Linear Systems