|
This article is cited in 36 scientific papers (total in 36 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
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
Citation:
Andrey Shilnikov, Leonid P. Shilnikov, Dmitry Turaev, “Blue-sky catastrophe in singularly perturbed systems”, Mosc. Math. J., 5:1 (2005), 269–282
Linking options:
https://www.mathnet.ru/eng/mmj193 https://www.mathnet.ru/eng/mmj/v5/i1/p269
|
Statistics & downloads: |
Abstract page: | 623 | References: | 85 |
|