Heteroclinic bifurcation

From Wikipedia, the free encyclopedia

This article or section does not cite its references or sources.
Please help improve this article by introducing appropriate citations. (help, get involved!) This article has been tagged since October 2006.

In mathematics, particularly dynamical systems, a heteroclinic bifurcation is a global bifurcation involving a heteroclinic cycle. Heteroclinic bifurcations come in two types, resonance bifurcations, and transverse bifurcations. Both types of bifurcation will result in the change of stability of the heteroclinic cycle.

At a resonance bifurcation, the stability of the cycle changes when an algebraic condition on the eigenvalues of the equilibria in the cycle is satisfied. This is usually accompanied by the birth or death of a periodic orbit.

A transverse bifurcation of a heteroclinic cycle is caused when the real part of a transverse eigenvalue of one of the equilibria in the cycle passes through zero. This will also cause a change in stability of the heteroclinic cycle.

Retrieved from "http://en.wikipedia.org../../../h/e/t/Heteroclinic_bifurcation.html"