Numerical computation of connecting orbits on a manifold

Numerical computation of connecting orbits on a manifold

0.00 Avg rating0 Votes
Article ID: iaor20126137
Volume: 61
Issue: 3
Start Page Number: 429
End Page Number: 464
Publication Date: Nov 2012
Journal: Numerical Algorithms
Authors: ,
Keywords: algebra
Abstract:

In this paper we propose a numerical method for approximating connecting orbits on a manifold and its bifurcation parameters. First we extend the standard nondegeneracy condition to the connecting orbits on a manifold. Then we construct a well‐posed system such that the nondegenerate connecting orbit pair on a manifold is its regular solution. We use a difference method to discretize the ODE part in this well‐posed system and we find that the numerical solutions still remain on the same manifold. We also set up a modified projection boundary condition to truncate connecting orbits on a manifold onto a finite interval. Then we prove the existence of truncated approximate connecting orbit pairs and derive error estimates. Finally, we carry out some numerical experiments to illustrate the theoretical estimates.

Reviews

Required fields are marked *. Your email address will not be published.