Geodesic
Blue sky catastrophe in systems with non-classical relaxation oscillations
Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 1, pp. 38-64

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The feasibility of a 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 they permit so-called nonclassic relaxation oscillations, that is, oscillations with slow components asymptotically close to time-discontinuous functions and a $\delta$-like fast component. Cases when blue-sky bifurcation leads to a relaxation cycle or stable two-dimensional torus are analyzed. Also the question of homoclinic structure emergence is considered.
Keywords: singularly perturbed system, relaxation cycle, asymptotic behavior, stability, non-classical relaxation oscillations.
Mots-clés : blue sky catastrophe 
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     title = {Blue sky catastrophe in systems  with non-classical relaxation oscillations},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {38--64},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2015_22_1_a2/}
}
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S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. Blue sky catastrophe in systems  with non-classical relaxation oscillations. Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 1, pp. 38-64. http://geodesic.mathdoc.fr/item/MAIS_2015_22_1_a2/