Two Limit Cycles in Liénard Piecewise Linear Differential Systems

Jaume Llibre; Enrique Ponce; Clàudia Valls

doi:10.1007/s00332-018-9523-5

Two Limit Cycles in Liénard Piecewise Linear Differential Systems

Jaume Llibre, Enrique Ponce, Clàudia Valls

Department of Mathematics

Research output: Contribution to journal › Article › Research

2 Citations (Scopus)

Abstract

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. Some techniques for studying the existence of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems. Rigorous new results are provided on the existence of two limit cycles surrounding the equilibrium point at the origin for systems with three zones separated by two parallel straight lines without symmetry. As a relevant application, it is shown the existence of bistable regimes in an asymmetric memristor-based electronic oscillator.

Original language	English
Pages (from-to)	1499-1522
Journal	Journal of Nonlinear Science
Volume	29
DOIs	https://doi.org/10.1007/s00332-018-9523-5
Publication status	Published - 15 Aug 2019

Keywords

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

Access to Document

10.1007/s00332-018-9523-5

Fingerprint Dive into the research topics of 'Two Limit Cycles in Liénard Piecewise Linear Differential Systems'. Together they form a unique fingerprint.

Cite this

@article{cba5631b22204bb18128702d665bbbd5,

title = "Two Limit Cycles in Li{\'e}nard Piecewise Linear Differential Systems",

abstract = "{\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature. Some techniques for studying the existence of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems. Rigorous new results are provided on the existence of two limit cycles surrounding the equilibrium point at the origin for systems with three zones separated by two parallel straight lines without symmetry. As a relevant application, it is shown the existence of bistable regimes in an asymmetric memristor-based electronic oscillator.",

keywords = "Limit cycles, Li{\'e}nard piecewise linear differential systems, Nonlinear control systems, Periodic orbits",

author = "Jaume Llibre and Enrique Ponce and Cl{\`a}udia Valls",

year = "2019",

month = aug,

day = "15",

doi = "10.1007/s00332-018-9523-5",

language = "English",

volume = "29",

pages = "1499--1522",

journal = "Journal of Nonlinear Science",

issn = "0938-8974",

publisher = "Springer New York",

}

TY - JOUR

T1 - Two Limit Cycles in Liénard Piecewise Linear Differential Systems

AU - Llibre, Jaume

AU - Ponce, Enrique

AU - Valls, Clàudia

PY - 2019/8/15

Y1 - 2019/8/15

N2 - © 2018, Springer Science+Business Media, LLC, part of Springer Nature. Some techniques for studying the existence of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems. Rigorous new results are provided on the existence of two limit cycles surrounding the equilibrium point at the origin for systems with three zones separated by two parallel straight lines without symmetry. As a relevant application, it is shown the existence of bistable regimes in an asymmetric memristor-based electronic oscillator.

AB - © 2018, Springer Science+Business Media, LLC, part of Springer Nature. Some techniques for studying the existence of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems. Rigorous new results are provided on the existence of two limit cycles surrounding the equilibrium point at the origin for systems with three zones separated by two parallel straight lines without symmetry. As a relevant application, it is shown the existence of bistable regimes in an asymmetric memristor-based electronic oscillator.

KW - Limit cycles

KW - Liénard piecewise linear differential systems

KW - Nonlinear control systems

KW - Periodic orbits

U2 - 10.1007/s00332-018-9523-5

DO - 10.1007/s00332-018-9523-5

M3 - Article

VL - 29

SP - 1499

EP - 1522

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

SN - 0938-8974

ER -