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On one bifurcation in relaxation systems

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Abstract

We establish conditions under which, in three-dimensional relaxation systems of the form {fx066-01}, where 0 < ε << 1, |μ| << 1, and ƒ, gC , the so-called “blue-sky catastrophe” is observed, i.e., there appears a stable relaxation cycle whose period and length tend to infinity as μ tends to a certain critical value μ*(ε), μ*(0) 0 = 0.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 63–72, January, 2008.

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Kolesov, A.Y., Mishchenko, E.F. & Rozov, N.K. On one bifurcation in relaxation systems. Ukr Math J 60, 66–77 (2008). https://doi.org/10.1007/s11253-008-0042-7

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  • DOI: https://doi.org/10.1007/s11253-008-0042-7

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