Journal
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
Volume 8, Issue 3, Pages 854-879Publisher
SIAM PUBLICATIONS
DOI: 10.1137/080741999
Keywords
invariant slow manifold; canard; collocation method; singular perturbaton
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Funding
- Department of Energy
- National Science Foundation
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Slow manifolds are important geometric structures in the state spaces of dynamical systems with multiple time scales. This paper introduces an algorithm for computing trajectories on slow manifolds that are normally hyperbolic with both stable and unstable fast manifolds. We present two examples of bifurcation problems where these manifolds play a key role and a third example in which saddle-type slow manifolds are part of a traveling wave pro. le of a partial differential equation. Initial value solvers are incapable of computing trajectories on saddle-type slow manifolds, so the slow manifold of saddle type (SMST) algorithm presented here is formulated as a boundary value method. We take an empirical approach here to assessing the accuracy and effectiveness of the algorithm.
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