Limit cycles for 3-monomial differential equations

Armengol Gasull; Chengzhi Li; Joan Torregrosa

doi:https://doi.org/10.1016/j.jmaa.2015.03.039

Limit cycles for 3-monomial differential equations

Armengol Gasull, Chengzhi Li, Joan Torregrosa

Department of Mathematics

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

4 Citations (Scopus)

Abstract

© 2015 Elsevier Inc. We study planar polynomial differential equations that in complex coordinates write as z ˙=Az+Bzkz-l+Czmz-n. We prove that for each p∈N there are differential equations of this type having at least p limit cycles. Moreover, for the particular case z ˙=Az+Bz-+Czmz-n, which has homogeneous nonlinearities, we show examples with several limit cycles and give a condition that ensures uniqueness and hyperbolicity of the limit cycle.

Original language	English
Pages (from-to)	735-749
Journal	Journal of Mathematical Analysis and Applications
Volume	428
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2015.03.039
Publication status	Published - 1 Jan 2015

Keywords

Abelian integrals
Bifurcations
Homogeneous nonlinearities
Limit cycles
Z<inf>q</inf>-equivariant symmetry

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title = "Limit cycles for 3-monomial differential equations",

abstract = "{\textcopyright} 2015 Elsevier Inc. We study planar polynomial differential equations that in complex coordinates write as z ˙=Az+Bzkz-l+Czmz-n. We prove that for each p∈N there are differential equations of this type having at least p limit cycles. Moreover, for the particular case z ˙=Az+Bz-+Czmz-n, which has homogeneous nonlinearities, we show examples with several limit cycles and give a condition that ensures uniqueness and hyperbolicity of the limit cycle.",

keywords = "Abelian integrals, Bifurcations, Homogeneous nonlinearities, Limit cycles, Z<inf>q</inf>-equivariant symmetry",

author = "Armengol Gasull and Chengzhi Li and Joan Torregrosa",

year = "2015",

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doi = "https://doi.org/10.1016/j.jmaa.2015.03.039",

language = "English",

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journal = "Journal of Mathematical Analysis and Applications",

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TY - JOUR

T1 - Limit cycles for 3-monomial differential equations

AU - Gasull, Armengol

AU - Li, Chengzhi

AU - Torregrosa, Joan

PY - 2015/1/1

Y1 - 2015/1/1

N2 - © 2015 Elsevier Inc. We study planar polynomial differential equations that in complex coordinates write as z ˙=Az+Bzkz-l+Czmz-n. We prove that for each p∈N there are differential equations of this type having at least p limit cycles. Moreover, for the particular case z ˙=Az+Bz-+Czmz-n, which has homogeneous nonlinearities, we show examples with several limit cycles and give a condition that ensures uniqueness and hyperbolicity of the limit cycle.

AB - © 2015 Elsevier Inc. We study planar polynomial differential equations that in complex coordinates write as z ˙=Az+Bzkz-l+Czmz-n. We prove that for each p∈N there are differential equations of this type having at least p limit cycles. Moreover, for the particular case z ˙=Az+Bz-+Czmz-n, which has homogeneous nonlinearities, we show examples with several limit cycles and give a condition that ensures uniqueness and hyperbolicity of the limit cycle.

KW - Abelian integrals

KW - Bifurcations

KW - Homogeneous nonlinearities

KW - Limit cycles

KW - Z<inf>q</inf>-equivariant symmetry

UR - https://ddd.uab.cat/record/145308

U2 - https://doi.org/10.1016/j.jmaa.2015.03.039

DO - https://doi.org/10.1016/j.jmaa.2015.03.039

M3 - Article

VL - 428

SP - 735

EP - 749

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -