Fenichel theory for multiple time scale singular perturbation problems
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This paper is concerned with a geometric study of singularly perturbed systems of ordinary differential equations expressed by (n-1)-parameter families of smooth vector fields on ℝl, where n ≥ 2. The inherent characteristic of such systems is the presence of an arbitrary number n of time scales. For n = 2, the proposed geometric approach in this paper reports to Fenichel theory of fast-slow systems [N. Fenichel, J. Differential Equations, 31 (1979), pp. 53-98]. We extend the three main theorems due to Fenichel [N. Fenichel, J. Differential Equations, 31 (1979), pp. 53-98] to systems involving any number of time scales.
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Fenichel theory, Multiple time scales, Singular perturbation
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Inglês
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SIAM Journal on Applied Dynamical Systems, v. 16, n. 3, p. 1425-1452, 2017.
