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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Igor FranovićNikola Burić

Abstract

We consider the coaction of two distinct noise sources on the activation process of a single excitable unit 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 or 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.

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Citations

Jun 8, 2017·Proceedings. Mathematical, Physical, and Engineering Sciences·Zhen ChenXianbin Liu
Sep 3, 2020·Chaos·Igor FranovićMatthias Wolfrum
Aug 4, 2020·Physical Review Letters·Vladimir KlinshovOtti D'Huys
Aug 3, 2018·Chaos·Igor FranovićMatthias Wolfrum
Jan 15, 2016·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Igor FranovićNikola Burić
Mar 23, 2018·Cognitive Neurodynamics·Jinjie Zhu, Xianbin Liu
Jan 20, 2018·Physical Review. E·Igor FranovićVladimir I Nekorkin

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