On the limit cycles of polynomial vector field

J. Llibre; G. Świrszcz

On the limit cycles of polynomial vector field

J. Llibre, G. Świrszcz

Departament de Matemàtiques

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Resum

In this paper we study the limit cycles which can bifurcate from the periodic orbits of the center located at the origin of the quadratic polynomial di®erential system x = -y(1+x), y= x(1+x), and of the cubic polynomial di®erential system x = -y(1-x2-y2), y= x(1-x 2-y2), when we perturb them in the class of all polynomial vector fields with quadratic and cubic homogenous nonlinearities, respectively. For doing this study we use the averaging theory. Copyright © 2011 Watam Press.

Idioma original	Anglès
Pàgines (de-a)	203-214
Revista	Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Volum	18
Número	2
Estat de la publicació	Publicada - 8 de febr. 2011

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title = "On the limit cycles of polynomial vector field",

abstract = "In this paper we study the limit cycles which can bifurcate from the periodic orbits of the center located at the origin of the quadratic polynomial di{\textregistered}erential system x = -y(1+x), y= x(1+x), and of the cubic polynomial di{\textregistered}erential system x = -y(1-x2-y2), y= x(1-x 2-y2), when we perturb them in the class of all polynomial vector fields with quadratic and cubic homogenous nonlinearities, respectively. For doing this study we use the averaging theory. Copyright {\textcopyright} 2011 Watam Press.",

keywords = "Averaging method, Center, Limit cycle, Periodic orbit, Reversible center",

author = "J. Llibre and G. {\'S}wirszcz",

year = "2011",

month = feb,

day = "8",

language = "English",

volume = "18",

pages = "203--214",

journal = "Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis",

issn = "1201-3390",

publisher = "Watam Press",

number = "2",

}

TY - JOUR

T1 - On the limit cycles of polynomial vector field

AU - Llibre, J.

AU - Świrszcz, G.

PY - 2011/2/8

Y1 - 2011/2/8

N2 - In this paper we study the limit cycles which can bifurcate from the periodic orbits of the center located at the origin of the quadratic polynomial di®erential system x = -y(1+x), y= x(1+x), and of the cubic polynomial di®erential system x = -y(1-x2-y2), y= x(1-x 2-y2), when we perturb them in the class of all polynomial vector fields with quadratic and cubic homogenous nonlinearities, respectively. For doing this study we use the averaging theory. Copyright © 2011 Watam Press.

AB - In this paper we study the limit cycles which can bifurcate from the periodic orbits of the center located at the origin of the quadratic polynomial di®erential system x = -y(1+x), y= x(1+x), and of the cubic polynomial di®erential system x = -y(1-x2-y2), y= x(1-x 2-y2), when we perturb them in the class of all polynomial vector fields with quadratic and cubic homogenous nonlinearities, respectively. For doing this study we use the averaging theory. Copyright © 2011 Watam Press.

KW - Averaging method

KW - Center

KW - Limit cycle

KW - Periodic orbit

KW - Reversible center

M3 - Article

SN - 1201-3390

VL - 18

SP - 203

EP - 214

JO - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

IS - 2

ER -

On the limit cycles of polynomial vector field

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