title: 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 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.
authors.affiliation: Scientific Computing Laboratory, Institute of Physics, University of Belgrade, P. O. Box 68, 11080 Beograd-Zemun, Serbia.
authors.forename: Igor
authors.initials: I
authors.lastname: Franović
authors.affiliation: Department of Physics and Mathematics, Faculty of Pharmacy, University of Belgrade, Vojvode Stepe 450, Belgrade, Serbia.
authors.forename: Kristina
authors.initials: K
authors.lastname: Todorović
authors.affiliation: Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška Cesta 160, SI-2000 Maribor, Slovenia.|Department of Physics, Faculty of Sciences, King Abdulaziz University, Jeddah, Saudi Arabia.
authors.forename: Matjaž
authors.initials: M
authors.lastname: Perc
authors.affiliation: Department of Applied Mathematics, Faculty of Mining and Geology, University of Belgrade, P. O. Box 162, Belgrade, Serbia.
authors.forename: Nebojša
authors.initials: N
authors.lastname: Vasović
authors.affiliation: Scientific Computing Laboratory, Institute of Physics, University of Beograd, P. O. Box 68, 11080 Beograd-Zemun, Serbia.
authors.forename: Nikola
authors.initials: N
authors.lastname: Burić