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Parabolic Bursting in an Excitable System Coupled with a Slow Oscillation
Abstract
We investigate the interaction of an excitable system with a slow oscillation. Under robust and general assumptions compatible with the more stringent assumptions usually made about excitable systems, we show that such a coupled system can display bursting, i.e. a stable solution in which some variable undergoes rapid oscillations followed by a period of quiescence, with both oscillation and quiescence continually repeated. Under a further weak condition, the bursting is “parabolic”, i.e. the local frequency of the fast oscillation increases and then decreases within a burst. The technique in this paper involves nonlinear changes of coordinates which transform the equations into ones which are closely related to Hill’s equation.
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Metadata
- Authors
- Ermentrout, G. B., & Kopell, N.
- Venue
- SIAM Journal on Applied Mathematics
- Published
- 1986-04
- Volume
- 46
- Issue
- 2
- Pages
- 233-253
- ISSN
- 0036-1399 (ISSN-L)
- 1095-712X
- OpenAlex
- W2072413244
- Cited by
- 596
- References
- 0
- FWCI
- 2.94
- Type
- journal article
- Language
- en
- Open access
- closed
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