On the zeros of the Abelian integrals for a class of Liénard systems

Tade, Moses, Tian, Yu-Chu, & Zhang, Tonghua (2006) On the zeros of the Abelian integrals for a class of Liénard systems. Physics Letters A, 358(4), pp. 262-274.

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Abstract

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

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ID Code: 23331
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: Limit Cycles, Lienard Systems, Bifurcation, Zeroes
DOI: 10.1016/j.physleta.2006.05.031
ISSN: 0375-9601
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Applied Mathematics not elsewhere classified (010299)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > COMPUTATION THEORY AND MATHEMATICS (080200) > Computation Theory and Mathematics not elsewhere classified (080299)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2006 Elsevier
Deposited On: 17 Jun 2009 13:50
Last Modified: 27 Sep 2016 00:27

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