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, which require mesh refinements to ensure uniform
convergence with respect to , 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 the computation of homoclinic
connections in the FitzHugh–Nagumo system.
Original language | English |
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Journal | S I A M Journal on Applied Dynamical Systems |
Volume | 14 |
Issue number | 2 |
Pages (from-to) | 1189–1227 |
ISSN | 1536-0040 |
DOIs | |
Publication status | Published - 2015 |
Keywords
- Slow-fast systems
- Slow manifolds of saddle type
- Reduction methods