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References (7)
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L. Cherkas (2007)
On an estimate of the number of limit cycles in a quadratic systemDifferential Equations, 43
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S. Chow, Chengzhi Li, Y. Yi (2000)
The Cyclicity of Period Annulus of Degenerate Quadratic Hamiltonian System with Elliptic Segment -
(1997)
The Dulac Function for Polynomial Autonomous Systems on the Plane -
A.A. Grin’, L.A. Cherkas (2005)
Extrema of the Andronov-Hopf Function of a Polynomial Lienard SystemDiffer. Uravn., 41
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(2000)
Dulac Function for Lienard System -
A. Grin, L. Cherkas (2005)
Extrema of the Andronov-Hopf function of a polynomial Lienard systemDifferential Equations, 41
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L.A. Cherkas (2007)
On an Estimate for the Number of Limit Cycles of a Quadratic SystemDiffer. Uravn., 43
- Publisher
- Springer Journals
- Copyright
- Copyright © 2012 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Partial Differential Equations; Difference and Functional Equations; Ordinary Differential Equations
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/S0012266112050072
- Publisher site
- See Article on Publisher Site
Abstract
The perturbed quadratic Hamiltonian system is reduced to a Lienard system with a small parameter for which a Dulac function depending on it is constructed. This permits one to estimate the number of limit cycles of the perturbed system for all sufficiently small parameter values. To find the Dulac function, we use the solution of a linear programming problem. The suggested method is used for studying three specific perturbed systems that have exactly two limit cycles, i.e., the distribution 2 or (0, 2), and one system with distribution (1, 1).
Journal
Differential Equations – Springer Journals
Published: Jul 4, 2012