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

Jaume Llibre; Enrique Ponce; Clàudia Valls

doi:https://doi.org/10.1007/s00332-015-9244-y

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

Jaume Llibre, Enrique Ponce, Clàudia Valls

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

20 Citations (Scopus)

Abstract

© 2015, Springer Science+Business Media New York. Some 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.

Original language	English
Pages (from-to)	861-887
Journal	Journal of Nonlinear Science
Volume	25
Issue number	4
DOIs	https://doi.org/10.1007/s00332-015-9244-y
Publication status	Published - 27 Aug 2015

Keywords

Limit cycles
Liénard piecewise linear differential systems
Nonlinear control systems
Periodic orbits

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AU - Ponce, Enrique

AU - Valls, Clàudia

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Y1 - 2015/8/27

N2 - © 2015, Springer Science+Business Media New York. Some 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.

AB - © 2015, Springer Science+Business Media New York. Some 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.

KW - Limit cycles

KW - Liénard piecewise linear differential systems

KW - Nonlinear control systems

KW - Periodic orbits

UR - https://ddd.uab.cat/record/145353

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DO - https://doi.org/10.1007/s00332-015-9244-y

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