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Noise-induced escape in an excitable system
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Khovanov, I. A., Polovinkin, A. V., Luchinsky, Dmitri G. and McClintock, P. V. E. (2013) Noise-induced escape in an excitable system. Physical Review E, Volume 87 (Number 3). 032116. doi:10.1103/PhysRevE.87.032116 ISSN 1539-3755.
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WRAP_Khovanov_PhysRevE.87.032116.pdf - Published Version Download (1397Kb) | Preview |
Official URL: http://dx.doi.org/10.1103/PhysRevE.87.032116
Abstract
We consider the stochastic dynamics of escape in an excitable system, the FitzHugh-Nagumo (FHN) neuronal model, for different classes of excitability. We discuss, first, the threshold structure of the FHN model as an example of a system without a saddle state. We then develop a nonlinear (nonlocal) stability approach based on the theory of large fluctuations, including a finite-noise correction, to describe noise-induced escape in the excitable regime. We show that the threshold structure is revealed via patterns of most probable (optimal) fluctuational paths. The approach allows us to estimate the escape rate and the exit location distribution. We compare the responses of a monostable resonator and monostable integrator to stochastic input signals and to a mixture of periodic and stochastic stimuli. Unlike the commonly used local analysis of the stable state, our nonlocal approach based on optimal paths yields results that are in good agreement with direct numerical simulations of the Langevin equation.
| Item Type: | Journal Article | ||||
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| Subjects: | Q Science > QA Mathematics R Medicine > RC Internal medicine > RC0321 Neuroscience. Biological psychiatry. Neuropsychiatry |
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| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering | ||||
| Library of Congress Subject Headings (LCSH): | Neurons -- Computer simulation, Neural networks (Neurobiology), Stochastic processes, Excitation (Physiology) | ||||
| Journal or Publication Title: | Physical Review E | ||||
| Publisher: | American Physical Society | ||||
| ISSN: | 1539-3755 | ||||
| Official Date: | March 2013 | ||||
| Dates: |
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| Volume: | Volume 87 | ||||
| Number: | Number 3 | ||||
| Article Number: | 032116 | ||||
| DOI: | 10.1103/PhysRevE.87.032116 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Date of first compliant deposit: | 24 December 2015 | ||||
| Date of first compliant Open Access: | 24 December 2015 | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), Rossiĭskiĭ fond fundamentalʹnykh issledovaniĭ [Russian Foundation for Basic Research] (RFBR) | ||||
| Grant number: | EP/C53932X/2 (EPSRC), EP/G070660/1 (EPSRC), 11-02-01418-a (RFFI) |
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