The Poincar ́e Bifurcation of the Non-Hamiltonian Quadratic Integrable System with One Center and One Unbounded Homoclinic Loop Formed by Cubics

Yan Song

doi:10.4028/www.scientific.net/AMR.694-697.288

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 694-697The Poincar ́e Bifurcation of the Non-Hamiltonian...

The Poincar ́e Bifurcation of the Non-Hamiltonian Quadratic Integrable System with One Center and One Unbounded Homoclinic Loop Formed by Cubics

Abstract:

In this paper, we investigate the Poincar ́e bifurcation of the non-Hamiltonian quadratic integrable system with one center and one unbounded homoclinic loop formed by cubics. It is proved that the cyclicity of the period annulus under quadratic perturbations is equal to two.

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Periodical:

Advanced Materials Research (Volumes 694-697)

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288-293

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.694-697.288

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Online since:

May 2013

Authors:

Yan Song

Keywords:

Abelian Integral, Non-Hamiltonian Quadratic Integrable System, Picard-Fuchs Equation, Poincar ́e Bifurcation

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