Limit cycles of polynomial differential equations with quintic homogeneous nonlinearities

Rebiha Benterki; Jaume Llibre

doi:10.1016/j.jmaa.2013.04.076

Limit cycles of polynomial differential equations with quintic homogeneous nonlinearities

Rebiha Benterki, Jaume Llibre

Department of Mathematics

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

8 Citations (Scopus)

Abstract

In this paper we mainly study the number of limit cycles which can bifurcate from the periodic orbits of the two centers ẋ=-y, ẏ=x; ẋ=-y(1-(x2+y2)2), ẏ=x(1-(x2+y2)2); when they are perturbed inside the class of all polynomial differential systems with quintic homogeneous nonlinearities. We do this study using the averaging theory of first, second and third orders. © 2013 Elsevier Ltd.

Original language	English
Pages (from-to)	16-22
Journal	Journal of Mathematical Analysis and Applications
Volume	407
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2013.04.076
Publication status	Published - 1 Nov 2013

Keywords

Averaging method
Center
Limit cycle
Periodic orbit
Reversible center

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title = "Limit cycles of polynomial differential equations with quintic homogeneous nonlinearities",

abstract = "In this paper we mainly study the number of limit cycles which can bifurcate from the periodic orbits of the two centers ẋ=-y, ẏ=x; ẋ=-y(1-(x2+y2)2), ẏ=x(1-(x2+y2)2); when they are perturbed inside the class of all polynomial differential systems with quintic homogeneous nonlinearities. We do this study using the averaging theory of first, second and third orders. {\textcopyright} 2013 Elsevier Ltd.",

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author = "Rebiha Benterki and Jaume Llibre",

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AU - Llibre, Jaume

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N2 - In this paper we mainly study the number of limit cycles which can bifurcate from the periodic orbits of the two centers ẋ=-y, ẏ=x; ẋ=-y(1-(x2+y2)2), ẏ=x(1-(x2+y2)2); when they are perturbed inside the class of all polynomial differential systems with quintic homogeneous nonlinearities. We do this study using the averaging theory of first, second and third orders. © 2013 Elsevier Ltd.

AB - In this paper we mainly study the number of limit cycles which can bifurcate from the periodic orbits of the two centers ẋ=-y, ẏ=x; ẋ=-y(1-(x2+y2)2), ẏ=x(1-(x2+y2)2); when they are perturbed inside the class of all polynomial differential systems with quintic homogeneous nonlinearities. We do this study using the averaging theory of first, second and third orders. © 2013 Elsevier Ltd.

KW - Averaging method

KW - Center

KW - Limit cycle

KW - Periodic orbit

KW - Reversible center

U2 - 10.1016/j.jmaa.2013.04.076

DO - 10.1016/j.jmaa.2013.04.076

M3 - Article

VL - 407

SP - 16

EP - 22

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

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ER -