Homoclinic orbits and Hopf points in forward-backward delay equations
by
Marc Georgi
Free University of Berlin

Forward-backward delay equations have recently attracted much attention. They typically arise as traveling wave equations of lattice-differential equations. In contrast to pure delay equations forward-backward delay equations are not well-posed. This talk focuses on a bifurcation of a homoclinic orbit to an asymptotic equilibrium, which undergoes a Hopf bifurcation. Using invariant manifolds we can successfully detect bifurcating solutions near the primary homoclinic orbit. This is the first time that such a global bifurcation is analysed in the setting of forward-backward delay equations.

Date received: June 28, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavj-11.