Abstract
We present a numerical method for branch switching between homoclinic orbits to equilibria of ODEs computed via numerical continuation. Starting from a 1-homoclinic orbit our method allows us to find and follow an N-homoclinic orbit, for any N>1 (if it exists nearby). This scheme is based on Lin's method and it is robust and reliable.
The method is implemented in AUTO/HOMCONT. A system of ordinary differential equations introduced by Sandstede featuring inclination and orbit flip bifurcations and homoclinic-doubling cascades, is used as a test bed for the algorithm. It is also successfully applied to reliably find multihump traveling wave solutions in the FitzHugh–Nagumo nerve-axon equations and in a fourth-order Hamiltonian system arising as a model for water waves.
The method is implemented in AUTO/HOMCONT. A system of ordinary differential equations introduced by Sandstede featuring inclination and orbit flip bifurcations and homoclinic-doubling cascades, is used as a test bed for the algorithm. It is also successfully applied to reliably find multihump traveling wave solutions in the FitzHugh–Nagumo nerve-axon equations and in a fourth-order Hamiltonian system arising as a model for water waves.
| Translated title of the contribution | Homoclinic branch switching: A numerical implementation of Lin's method |
|---|---|
| Original language | English |
| Pages (from-to) | 2977-2999 |
| Number of pages | 23 |
| Journal | International Journal of Bifurcation and Chaos |
| Volume | 13 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 2003 |
Research Groups and Themes
- Engineering Mathematics Research Group
Keywords
- Homoclinic bifurcations
- numerical continuation
- branch switching