THE DYNAMICS OF SLOW MANIFOLDS

Ferdinand Verhulst, Taoufik Bakri

Abstract


After reviewing a number of results from geometric singular perturbation theory, we discuss several approaches to obtain periodic solutions in a slow manifold.Regarding nonhyperbolic transitions we consider relaxation oscillations and canard-like solutions. The results are illustrated by prey-predator systems.

DOI : http://dx.doi.org/10.22342/jims.13.1.76.73-90


Keywords


singular perturbations, slow manifolds, periodic solutions, canards, relaxation oscillations



DOI: https://doi.org/10.22342/jims.13.1.76.73-90

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Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
Senolowo, Sinduadi, Mlati, Sleman Regency, Special Region of Yogyakarta 55281, Telp. (0274) 552243
Email: jims.indoms@gmail.com


p-ISSN: 2086-8952 | e-ISSN: 2460-0245


Journal of the Indonesian Mathematical Society is licensed under a Creative Commons Attribution 4.0 International License

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