Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1888884 | Chaos, Solitons & Fractals | 2009 | 9 Pages |
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.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Qiuying Lu,