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arXiv · 1403.6583

Computation of saddle type slow manifolds using iterative methods

Kristian Uldall Kristiansen
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Abstract

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that require mesh refinements to ensure uniform convergence with respect to $\epsilon$, appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples including: A model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables and to the computation of homoclinic connections in the FitzHugh-Nagumo system.

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Kristian Uldall Kristiansen. 2014-03-26. Computation of saddle type slow manifolds using iterative methods. https://arxiv.org/abs/1403.6583

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