Activation process in excitable systems with multiple noise sources: One and two interacting units

TL;DR

This paper investigates how two different noise sources influence the activation process in excitable systems modeled by Fitzhugh-Nagumo equations, focusing on single and coupled units, and explores the effects on activation paths and statistical features.

Contribution

It introduces a method to determine most probable activation paths with relevant boundary conditions for class II excitable units, applicable to both single and coupled systems.

Findings

Most probable activation paths are identified for different noise interactions.

The effects of linear and nonlinear interactions on activation statistics are characterized.

Universal properties related to stochastic bifurcations are discussed.

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.