Article ID Journal Published Year Pages File Type
842297 Nonlinear Analysis: Theory, Methods & Applications 2008 13 Pages PDF
Abstract

In this work, bifurcations in the class that the homoclinic orbit connects the strong stable and strong unstable manifolds of a saddle are investigated for four-dimensional vector fields. The existence, numbers, coexistence and incoexistence of 1-homoclinic orbit, 1-periodic orbit, 2n2n-homoclinic orbit and 2n2n-periodic orbit are obtained, the approximate expressions of the corresponding bifurcation surfaces and the bifurcation diagrams are also presented.

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