Activation process in excitable systems with multiple noise sources: One and two interacting units
Abstract
We consider the coaction of two distinct noise sources on the activation process of a single and two interacting excitable units, which are mathematically described by the Fitzhugh-Nagumo equations. We determine the most probable activation paths around which the corresponding stochastic trajectories are clustered. The key point lies in introducing appropriate boundary conditions that are relevant for a class II excitable unit, which can be immediately generalized also to scenarios involving two coupled units. We analyze the effects of the two noise sources on the statistical features of the activation process, in particular demonstrating how these are modified due to the linear/nonlinear form of interactions. Universal properties of the activation process are qualitatively discussed in the light of a stochastic bifurcation that underlies the transition from a stochastically stable fixed point to continuous oscillations.
Keywords
Cite
@article{arxiv.1507.03260,
title = {Activation process in excitable systems with multiple noise sources: One and two interacting units},
author = {Igor Franović and Kristina Todorović and Matjaz Perc and Nebojša Vasović and Nikola Burić},
journal= {arXiv preprint arXiv:1507.03260},
year = {2016}
}
Comments
18 two-column pages, 9 figures; accepted for publication in Physical Review E