Uniqueness and Non-uniqueness of Limit Cycles for Piecewise Linear Differential Systems with Three Zones and No Symmetry

El títol de la versió pre-print de l'article és: Limit cycles of piecewise linear differential systems with three zones and symmetAgraïments: The first author is partially supported by a FEDER-UNAB10-4E-378Some techniques for proving the existence and uniqueness of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems with two and three zones and no symmetry. For planar systems with three linearity zones, the existence of two limit cycles surrounding the only equilibrium point at the origin is rigorously shown for the first time. The usefulness of the achieved analytical results is illustrated by considering non-symmetric memristor-based electronic oscillators

Limit cycles in planar piecewise linear Hamiltonian systems with three zones without equilibrium points

We study the existence of limit cycles in planar piecewise linear Hamiltonian systems with three zones without equilibrium points. In this scenario, we have shown that such systems have at most one crossing limit cycle

Phase portraits of continuous piecewise linear Liénard differential systems with three zones

Phase portraits are an invaluable tool in studying differential systems. Most of known results about global phase portraits are related to the smooth differential systems. This paper deals with a class of planar continuous piecewise linear Liénard differential systems with three zones separated by two vertical lines without symmetry. We provide the topological classification of the phase portraits in the Poincaré disc for systems having a unique singular point located in the middle zone

Phase portraits of piecewise linear continuous differential systems with two zones separated by a straight line

This paper provides the classification of the phase portraits in the Poincaré disc of all piecewise linear continuous differential systems with two zones separated by a straight line having a unique finite singular point which is a node or a focus. The sufficient and necessary conditions for existence and uniqueness of limit cycles are also given

Uniqueness and Non-uniqueness of Limit Cycles for Piecewise Linear Differential Systems with Three Zones and No Symmetry

El títol de la versió pre-print de l'article és: Limit cycles of piecewise linear differential systems with three zones and symmetAgraïments: The first author is partially supported by a FEDER-UNAB10-4E-378Some techniques for proving the existence and uniqueness of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems with two and three zones and no symmetry. For planar systems with three linearity zones, the existence of two limit cycles surrounding the only equilibrium point at the origin is rigorously shown for the first time. The usefulness of the achieved analytical results is illustrated by considering non-symmetric memristor-based electronic oscillators