Non-resonance 3D homoclinic bifurcation with an inclination flip

Qiuying Lu

Chaos, Solitons & Fractals, 2009, vol. 42, issue 5, 2597-2605

Abstract: Local active coordinates approach is employed to study the bifurcation of a non-resonance three-dimensional smooth system which has a homoclinic orbit to a hyperbolic equilibrium point with three real eigenvalues -α,-β,1 satisfying α>β>0. A homoclinic orbit is called an inclination-flip homoclinic orbit if the strong inclination property of the stable manifold is violated. In this paper, we show the existence of 1-homoclinic orbit, 1-periodic orbit, 2n-homoclinic orbit and 2n-periodic orbit in the unfolding of an inclination-flip homoclinic orbit. And we figure out the bifurcation diagram based on the existence region of the corresponding bifurcation.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:42:y:2009:i:5:p:2597-2605

DOI: 10.1016/j.chaos.2009.03.112

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