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2009•Journal of Fuyang Teachers CollegeRequires access

The homoclinic bifurcations of a class of planar cubic systems

MU Yang-mei

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Abstract

In this paper,by using the bifurcation method to analyze the relative distance between the stable manifold and the unstable manifold after the homoclinic orbit of the unperturbed system is perturbed to break,the author studies the existing problem of limit cycles of a class of planar cubic systems,and gives the existence conditions of limit cycles.

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What this paper is about

In this paper,by using the bifurcation method to analyze the relative distance between the stable manifold and the unstable manifold after the homoclinic orbit of the unperturbed system is perturbed to break,the author studies the existing problem of limit cycles of a class of planar cubic systems,and gives the existence conditions of limit cycles.

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Available abstract

In this paper,by using the bifurcation method to analyze the relative distance between the stable manifold and the unstable manifold after the homoclinic orbit of the unperturbed system is perturbed to break,the author studies the existing problem of limit cycles of a class of planar cubic systems,and gives the existence conditions of limit cycles.

Key concepts: Homoclinic orbit, Homoclinic bifurcation, Planar, Heteroclinic orbit, Limit (mathematics), Stable manifold, Manifold (fluid mechanics), Class (philosophy)

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