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Moscow Mathematical Journal, 2005, Volume 5, Number 1, Pages 269–282
DOI: https://doi.org/10.17323/1609-4514-2005-5-1-269-282 (Mi mmj193) 		 
This article is cited in 35 scientific papers (total in 35 papers)

Blue-sky catastrophe in singularly perturbed systems

Andrey Shilnikova, Leonid P. Shilnikovb, Dmitry Turaevc

a Department of Mathematics and Statistics, Georgia State University, Atlanta, USA
b Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia
c Department of Mathematics, Ben Gurion University of the Negev, ISRAEL
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DOI: https://doi.org/10.17323/1609-4514-2005-5-1-269-282
Abstract: We show that the blue-sky catastrophe, which creates a stable periodic orbit of unboundedly increasing length, is a typical phenomenon for singularly perturbed (multi-scale) systems with at least two fast variables. Three distinct mechanisms of this bifurcation are described. We argue that it is behind the transition from periodic spiking to periodic bursting oscillations.
Key words and phrases: Saddle-node, global bifurcations, stability boundaries, slow-fast system, bursting oscillations, spikes, excitability.
Received: April 23, 2003
Bibliographic databases:
MSC: 37G15, 34E15, 37C27, 34C26
Language: English
Citation: Andrey Shilnikov, Leonid P. Shilnikov, Dmitry Turaev, “Blue-sky catastrophe in singularly perturbed systems”, Mosc. Math. J., 5:1 (2005), 269–282
Citation in format AMSBIB
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\by Andrey~Shilnikov, Leonid~P.~Shilnikov, Dmitry~Turaev
\paper Blue-sky catastrophe in singularly perturbed systems
\jour Mosc. Math.~J.
\yr 2005
\vol 5
\issue 1
\pages 269--282
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2153476}
\zmath{https://zbmath.org/?q=an:1092.37030}
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