Knobloch, J. and Wagenknecht, T. (2007) Snaking of multiple homoclinic orbits in reversible systems. [MIMS Preprint]
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Abstract
We study N-homoclinic orbits near a heteroclinic cycle in a reversible system. The cycle is assumed to connect two equilibria of saddle-focus type. Using Lin's method we establish the existence of infinitely many N-homoclinic orbits for each N near the cycle. In particular, these orbits exist along snaking curves, thus mirroring the behaviour one-homoclinic orbits. The general analysis is illustrated by numerical studies for a Swift-Hohenberg system.
| Item Type: | MIMS Preprint |
|---|---|
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 34 Ordinary differential equations MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory |
| Depositing User: | Thomas Wagenknecht |
| Date Deposited: | 14 Aug 2007 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/832 |
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