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Blue sky catastrophe in systems with nonclassical relaxation oscillations

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Abstract

The feasibility of the well-known blue sky bifurcation in a class of three-dimensional singularly perturbed systems of ordinary differential equations with one fast and two slow variables is studied. A characteristic property of the considered systems is that so-called nonclassical relaxation oscillations occur in them. The same name is used for oscillations with slow components, which are asymptotically close to some time-discontinuous functions and a δ-like fast component. Cases when the blue sky catastrophe results in a stable relaxation cycle or a stable two-dimensional invariant torus are analyzed. The problem of the appearance of homoclinic structures is also considered.

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Authors and Affiliations

  1. Demidov Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia

    S. D. Glyzin & A. Yu. Kolesov

  2. Chernogolovka Scientific Center, Russian Academy of Sciences, ul. Lesnaya 9, Chernogolovka, Moscow oblast, 142432, Russia

    S. D. Glyzin

  3. Moscow State University, Moscow, 119991, Russia

    N. Kh. Rozov

Authors
  1. S. D. Glyzin
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  2. A. Yu. Kolesov
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  3. N. Kh. Rozov
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Correspondence to S. D. Glyzin.

Additional information

Original Russian Text © S.D. Glyzin, A.Yu. Kolesov, N.Kh. Rozov, 2015, published in Modelirovanie i Analiz Informatsionnykh Sistem, 2015, No. 1, pp. 38–64.

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Glyzin, S.D., Kolesov, A.Y. & Rozov, N.K. Blue sky catastrophe in systems with nonclassical relaxation oscillations. Aut. Control Comp. Sci. 49, 525–546 (2015). https://doi.org/10.3103/S0146411615070081

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  • DOI: https://doi.org/10.3103/S0146411615070081

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