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The influence of the integral manifold shape on the onset of relaxation oscillations

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Abstract

The relaxation oscillations are studied of a singularly perturbed system of ordinary differential equations with m slow and n fast variables (m × n) in the two cases: (1) m = n = 1 (1 × 1) and (2) m = 2, n = 1 (2 × 1). As sufficient conditions for the existence of relaxation oscillations there some general class is described of the functions determining the slow manifold for this system.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    L. I. Kononenko

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  1. L. I. Kononenko
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Correspondence to L. I. Kononenko.

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Original Russian Text © L.I. Kononenko, 2006, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2006, Vol. IX, No. 2(28), pp. 75–80.

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Kononenko, L.I. The influence of the integral manifold shape on the onset of relaxation oscillations. J. Appl. Ind. Math. 2, 508–512 (2008). https://doi.org/10.1134/S1990478908040078

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  • DOI: https://doi.org/10.1134/S1990478908040078

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