Limit cycles for a variant of a generalized Riccati equation

Jaume Llibre; Claudia Valls

doi:10.1016/j.aml.2016.11.016

Limit cycles for a variant of a generalized Riccati equation

Jaume Llibre, Claudia Valls

Departament de Matemàtiques

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© 2017 Elsevier Ltd In this paper we provide a lower bound for the maximum number of limit cycles surrounding the origin of systems (ẋ,ẏ=ẍ) given by a variant of the generalized Riccati equation ẍ+εx2n+1ẋ+bx4n+3=0,where b>0, b∈R, n is a non-negative integer and ε is a small parameter. The tool for proving this result uses Abelian integrals.

Idioma original	Anglès
Pàgines (de-a)	76-79
Revista	Applied Mathematics Letters
Volum	68
DOIs	https://doi.org/10.1016/j.aml.2016.11.016
Estat de la publicació	Publicada - 1 de juny 2017

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10.1016/j.aml.2016.11.016

https://ddd.uab.cat/record/182520

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title = "Limit cycles for a variant of a generalized Riccati equation",

abstract = "{\textcopyright} 2017 Elsevier Ltd In this paper we provide a lower bound for the maximum number of limit cycles surrounding the origin of systems (ẋ,ẏ=ẍ) given by a variant of the generalized Riccati equation ẍ+εx2n+1ẋ+bx4n+3=0,where b>0, b∈R, n is a non-negative integer and ε is a small parameter. The tool for proving this result uses Abelian integrals.",

keywords = "Abelian integral, Generalized Riccati system, Limit cycles, Weak 16th Hilbert problem",

author = "Jaume Llibre and Claudia Valls",

year = "2017",

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doi = "10.1016/j.aml.2016.11.016",

language = "English",

volume = "68",

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journal = "Applied Mathematics Letters",

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publisher = "Elsevier Limited",

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T1 - Limit cycles for a variant of a generalized Riccati equation

AU - Llibre, Jaume

AU - Valls, Claudia

PY - 2017/6/1

Y1 - 2017/6/1

N2 - © 2017 Elsevier Ltd In this paper we provide a lower bound for the maximum number of limit cycles surrounding the origin of systems (ẋ,ẏ=ẍ) given by a variant of the generalized Riccati equation ẍ+εx2n+1ẋ+bx4n+3=0,where b>0, b∈R, n is a non-negative integer and ε is a small parameter. The tool for proving this result uses Abelian integrals.

AB - © 2017 Elsevier Ltd In this paper we provide a lower bound for the maximum number of limit cycles surrounding the origin of systems (ẋ,ẏ=ẍ) given by a variant of the generalized Riccati equation ẍ+εx2n+1ẋ+bx4n+3=0,where b>0, b∈R, n is a non-negative integer and ε is a small parameter. The tool for proving this result uses Abelian integrals.

KW - Abelian integral

KW - Generalized Riccati system

KW - Limit cycles

KW - Weak 16th Hilbert problem

U2 - 10.1016/j.aml.2016.11.016

DO - 10.1016/j.aml.2016.11.016

M3 - Article

SN - 0893-9659

VL - 68

SP - 76

EP - 79

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

Limit cycles for a variant of a generalized Riccati equation

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