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On the zeros of the Abelian integrals for a class of Liénard systems by Tonghua Zhang; Moses O. Tadé; Yu-Chu Tian is a Physics and Astronomy article available to read on EtoBox.

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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 Letter, we investigated a class of Liénard systems of the form ẋ = y, ẏ = f (x) + yg(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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Author

Tonghua Zhang; Moses O. Tadé; Yu-Chu Tian

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0375-9601)

Published

2006

Language

EN

Field

Physics and Astronomy (Physical Sciences)