On limit cycles bifurcating from the infinity in discontinuous piecewise linear differential systems

Márcio R.A. Gouveia; Jaume Llibre; Douglas D. Novaes

doi:10.1016/j.amc.2015.09.022

On limit cycles bifurcating from the infinity in discontinuous piecewise linear differential systems

Márcio R.A. Gouveia, Jaume Llibre, Douglas D. Novaes

Department of Mathematics

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

7 Citations (Scopus)

Abstract

© 2015 Elsevier Inc. All rights reserved. In this paper we consider the linear differential center (x,y)=(-y,x) perturbed inside the class of all discontinuous piecewise linear differential systems with two zones separated by the straight line y=0. Using the Bendixson transformation we provide sufficient conditions to ensure the existence of a crossing limit cycle coming purely from the infinity. We also study the displacement function for a class of discontinuous piecewise smooth differential system.

Original language	English
Pages (from-to)	365-374
Journal	Applied Mathematics and Computation
Volume	271
DOIs	https://doi.org/10.1016/j.amc.2015.09.022
Publication status	Published - 15 Nov 2015

Keywords

Discontinuous differential system
Displacement function
Infinite periodic orbit
Limit cycle
Piecewise linear differential system

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title = "On limit cycles bifurcating from the infinity in discontinuous piecewise linear differential systems",

abstract = "{\textcopyright} 2015 Elsevier Inc. All rights reserved. In this paper we consider the linear differential center (x,y)=(-y,x) perturbed inside the class of all discontinuous piecewise linear differential systems with two zones separated by the straight line y=0. Using the Bendixson transformation we provide sufficient conditions to ensure the existence of a crossing limit cycle coming purely from the infinity. We also study the displacement function for a class of discontinuous piecewise smooth differential system.",

keywords = "Discontinuous differential system, Displacement function, Infinite periodic orbit, Limit cycle, Piecewise linear differential system",

author = "Gouveia, {M{\'a}rcio R.A.} and Jaume Llibre and Novaes, {Douglas D.}",

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AU - Gouveia, Márcio R.A.

AU - Llibre, Jaume

AU - Novaes, Douglas D.

PY - 2015/11/15

Y1 - 2015/11/15

N2 - © 2015 Elsevier Inc. All rights reserved. In this paper we consider the linear differential center (x,y)=(-y,x) perturbed inside the class of all discontinuous piecewise linear differential systems with two zones separated by the straight line y=0. Using the Bendixson transformation we provide sufficient conditions to ensure the existence of a crossing limit cycle coming purely from the infinity. We also study the displacement function for a class of discontinuous piecewise smooth differential system.

AB - © 2015 Elsevier Inc. All rights reserved. In this paper we consider the linear differential center (x,y)=(-y,x) perturbed inside the class of all discontinuous piecewise linear differential systems with two zones separated by the straight line y=0. Using the Bendixson transformation we provide sufficient conditions to ensure the existence of a crossing limit cycle coming purely from the infinity. We also study the displacement function for a class of discontinuous piecewise smooth differential system.

KW - Discontinuous differential system

KW - Displacement function

KW - Infinite periodic orbit

KW - Limit cycle

KW - Piecewise linear differential system

U2 - 10.1016/j.amc.2015.09.022

DO - 10.1016/j.amc.2015.09.022

M3 - Article

VL - 271

SP - 365

EP - 374

ER -