Nonreversible Homoclinic Snaking

Details Nonreversible Homoclinic Snaking Nonreversible Homoclinic Snaking

2010-11-30

arxiv.org/abs/1011.6546v1

Mathematics

Dynamical Systems

Scientific paper

Homoclinic snaking refers to the sinusoidal snaking continuation curve of homoclinic orbits near a heteroclinic cycle connecting an equilibrium E and a periodic orbit P. Along this curve the homoclinic orbit performs more and more windings about the periodic orbit. Typically this behaviour appears in reversible Hamiltonian systems. Here we discuss this phenomenon in systems without any particular structure. We give a rigorous analytical verification of homoclinic snaking under certain assumptions on the behaviour of the stable and unstable manifolds of E and P. We show how the snaking behaviour depends on the signs of the Floquet multipliers of P. Further we present a nonsnaking scenario. Finally we show numerically that these assumptions are fulfilled in a model equation.

Affiliated with

Also associated with

No associations

Rating

Nonreversible Homoclinic Snaking does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nonreversible Homoclinic Snaking, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonreversible Homoclinic Snaking will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-445356