Oscillations and Random Perturbations of a FitzHugh-Nagumo System
Catherine Doss (LJLL), Mich\`ele Thieullen (PMA)
TL;DR
This paper investigates how stochastic perturbations can induce oscillations and alter bifurcation behavior in the FitzHugh-Nagumo system, revealing new dynamics not present in the deterministic model.
Contribution
It demonstrates that noise can generate oscillations and create new equilibrium points and bifurcations in the FitzHugh-Nagumo system, expanding understanding of stochastic effects.
Findings
Noise induces oscillations in parameter regimes where the deterministic system is stable.
New equilibrium points emerge due to stochastic perturbations.
Bifurcation parameters are altered by the presence of noise.
Abstract
We consider a stochastic perturbation of a FitzHugh-Nagumo system. We show that it is possible to generate oscillations for values of parameters which do not allow oscillations for the deterministic system. We also study the appearance of a new equilibrium point and new bifurcation parameters due to the noisy component.
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Taxonomy
Topicsstochastic dynamics and bifurcation · Nonlinear Dynamics and Pattern Formation · Advanced Thermodynamics and Statistical Mechanics