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Stochastic hierarchical systems: excitable dynamics

Item Type:Article
Title:Stochastic hierarchical systems: excitable dynamics
Creators Name:Leonhardt, H., Zaks, M.A., Falcke, M. and Schimansky-Geier, L.
Abstract:We present a discrete model of stochastic excitability by a low-dimensional set of delayed integral equations governing the probability in the rest state, the excited state, and the refractory state. The process is a random walk with discrete states and nonexponential waiting time distributions, which lead to the incorporation of memory kernels in the integral equations. We extend the equations of a single unit to the system of equations for an ensemble of globally coupled oscillators, derive the mean field equations, and investigate bifurcations of steady states. Conditions of destabilization are found, which imply oscillations of the mean fields in the stochastic ensemble. The relation between the mean field equations and the paradigmatic Kuramoto model is shown.
Keywords:Excitable Systems, Delayed Integral Equations, Time-Convoluted Master Equations
Source:Journal of Biological Physics
Page Range:521-538
Date:October 2008
Official Publication:https://doi.org/10.1007/s10867-008-9112-1
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