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Nelin. Dinam., 2013, Volume 9, Number 2, Pages 295–307 (Mi nd391)  

This article is cited in 4 scientific papers (total in 4 papers)

Splitting bifurcation of stochastic cycles in the FitzHugh–Nagumo model

Irina A. Bashkirtseva, Lev B. Ryashko, Evdokia S. Slepukhina

Ural Federal University, Ekaterinburg, Russia

Abstract: We study the stochastic dynamics of FitzHugh–Nagumo model in the zone of limit cycles. For weak noise, random trajectories are concentrated in a small neighborhood of the initial deterministic unperturbed orbit of the limit cycle. As noise increases, in the zone of Canard cycles of the FitzHugh–Nagumo model, the bundle of random trajectories begins to split into two parts. This phenomenon is investigated using the density distribution of random trajectories. It is shown that the threshold noise intensity corresponding to the splitting bifurcation depends essentially on the degree of the stochastic sensitivity of the cycle. Using the stochastic sensitivity functions technique, a critical value corresponding to the supersensitive cycle is found and comparative parametric analysis of the effect of the stochastic cycle splitting in the vicinity of the critical value is carried out.

Keywords: FitzHugh–Nagumo model, stochastic sensitivity, cycles, splitting bifurcation.

Full text: PDF file (1253 kB)
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UDC: 531.36
MSC: 37H20, 60H10
Received: 18.02.2013
Revised: 15.05.2013

Citation: Irina A. Bashkirtseva, Lev B. Ryashko, Evdokia S. Slepukhina, “Splitting bifurcation of stochastic cycles in the FitzHugh–Nagumo model”, Nelin. Dinam., 9:2 (2013), 295–307

Citation in format AMSBIB
\Bibitem{BasRyaSle13}
\by Irina~A.~Bashkirtseva, Lev~B.~Ryashko, Evdokia~S.~Slepukhina
\paper Splitting bifurcation of stochastic cycles in the FitzHugh--Nagumo model
\jour Nelin. Dinam.
\yr 2013
\vol 9
\issue 2
\pages 295--307
\mathnet{http://mi.mathnet.ru/nd391}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. B. Ryashko, E. S. Slepukhina, “Stokhasticheskaya generatsiya kolebanii bolshikh amplitud v dvumernoi modeli Khindmarsh–Roze”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 2, 76–85  mathnet
    2. L. B. Ryashko, E. S. Slepukhina, “Analiz indutsirovannykh shumom pachechnykh kolebanii v dvumernoi modeli Khindmarsh-Roze”, Kompyuternye issledovaniya i modelirovanie, 6:4 (2014), 605–619  elib
    3. L. B. Ryashko, E. S. Slepukhina, “Analiz indutsirovannykh shumom pachechnykh kolebanii v dvumernoi modeli Khindmarsh-Roze”, Kompyuternye issledovaniya i modelirovanie, 6:4 (2014), 605–619  mathnet
    4. A. V. Kazarnikov, S. V. Revina, “Vozniknovenie avtokolebanii v sisteme Releya s diffuziei”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:2 (2016), 16–28  mathnet  crossref  elib
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