Limit cycles of discontinuous piecewise polynomial vector fields

Tiago de Carvalho; Jaume Llibre; Durval José Tonon

doi:https://doi.org/10.1016/j.jmaa.2016.11.048

Limit cycles of discontinuous piecewise polynomial vector fields

Tiago de Carvalho, Jaume Llibre, Durval José Tonon

Department of Mathematics

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

2 Citations (Scopus)

Abstract

© 2016 Elsevier Inc. When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x˙=−y((x2+y2)/2)m and y˙=x((x2+y2)/2)m with m≥1, when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces. The positive integers m, n and k are arbitrary. The main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields.

Original language	English
Pages (from-to)	572-579
Journal	Journal of Mathematical Analysis and Applications
Volume	449
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2016.11.048
Publication status	Published - 1 May 2017

Keywords

Averaging theory
Cyclicity
Limit cycle
Piecewise smooth vector fields

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AU - de Carvalho, Tiago

AU - Llibre, Jaume

AU - Tonon, Durval José

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N2 - © 2016 Elsevier Inc. When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x˙=−y((x2+y2)/2)m and y˙=x((x2+y2)/2)m with m≥1, when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces. The positive integers m, n and k are arbitrary. The main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields.

AB - © 2016 Elsevier Inc. When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x˙=−y((x2+y2)/2)m and y˙=x((x2+y2)/2)m with m≥1, when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces. The positive integers m, n and k are arbitrary. The main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields.

KW - Averaging theory

KW - Cyclicity

KW - Limit cycle

KW - Piecewise smooth vector fields

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JF - Journal of Mathematical Analysis and Applications

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