The following model is an example of a three-dimensional vector field exhibiting all types of homoclinic bifurcations. It was developed by Björn Sandstede and in a simplified form, the equations are

We choose fixed parameters *a = 0.125*, *b = 0.875*,
*c = -2*, *= 1*, *= 1*, and *= 3*. The parameter is the continuation parameter.

The origin is always an equilibrium. For *< 0* a twisted saddle periodic orbit
exists that disappears in a twisted homoclinic bifurcation at *= 0*.

The animated gif shows the unstable manifold
rotating about the z-axis, centered at B
(3.4MB). |

Copyright © 2001 by Hinke Osinga

Last modified: Tue Oct 30 16:04:36 2001