Journal
JOURNAL OF NONLINEAR SCIENCE
Volume 30, Issue 6, Pages 3161-3198Publisher
SPRINGER
DOI: 10.1007/s00332-020-09647-4
Keywords
Multiple timescale dynamical systems; Singularity theory
Categories
Funding
- Australian Research Council [DP180103022]
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We develop the contact singularity theory for singularly perturbed (or 'slow-fast') vector fields of the general form z' = H(z, epsilon), z is an element of R-n and 0 < epsilon << 1. Our main result is the derivation of computable, coordinate-independent defining equations for contact singularities under an assumption that the leading-order term of the vector field admits a suitable factorization. This factorization can in turn be computed explicitly in a wide variety of applications. We demonstrate these computable criteria by locating contact folds and, for the first time, contact cusps in general slow-fast models of biochemical oscillators and the Yamada model for self-pulsating lasers.
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