Geodesic
Splitting bifurcation of stochastic cycles in the FitzHugh--Nagumo model
Russian journal of nonlinear dynamics, Tome 9 (2013) no. 2, pp. 295-307

Voir la notice de l'article provenant de la source Math-Net.Ru

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, splitting bifurcation.
Mots-clés : cycles 
@article{ND_2013_9_2_a6,
     author = {Irina A. Bashkirtseva and Lev B. Ryashko and Evdokia S. Slepukhina},
     title = {Splitting bifurcation of stochastic cycles in the {FitzHugh--Nagumo} model},
     journal = {Russian journal of nonlinear dynamics},
     pages = {295--307},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2013_9_2_a6/}
}
TY  - JOUR
AU  - Irina A. Bashkirtseva
AU  - Lev B. Ryashko
AU  - Evdokia S. Slepukhina
TI  - Splitting bifurcation of stochastic cycles in the FitzHugh--Nagumo model
JO  - Russian journal of nonlinear dynamics
PY  - 2013
SP  - 295
EP  - 307
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2013_9_2_a6/
LA  - ru
ID  - ND_2013_9_2_a6
ER  - 
%0 Journal Article
%A Irina A. Bashkirtseva
%A Lev B. Ryashko
%A Evdokia S. Slepukhina
%T Splitting bifurcation of stochastic cycles in the FitzHugh--Nagumo model
%J Russian journal of nonlinear dynamics
%D 2013
%P 295-307
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2013_9_2_a6/
%G ru
%F ND_2013_9_2_a6
Irina A. Bashkirtseva; Lev B. Ryashko; Evdokia S. Slepukhina. Splitting bifurcation of stochastic cycles in the FitzHugh--Nagumo model. Russian journal of nonlinear dynamics, Tome 9 (2013) no. 2, pp. 295-307. http://geodesic.mathdoc.fr/item/ND_2013_9_2_a6/