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Non-Markovian approach to globally coupled excitable systems

Item Type:Article
Title:Non-Markovian approach to globally coupled excitable systems
Creators Name:Prager, T. and Falcke, M. and Schimansky-Geier, L. and Zaks, M.A.
Abstract:We consider stochastic excitable units with three discrete states. Each state is characterized by a waiting time density function. This approach allows for a non-Markovian description of the dynamics of separate excitable units and of ensembles of such units. We discuss the emergence of oscillations in a globally coupled ensemble with excitatory coupling. In the limit of a large ensemble we derive the non-Markovian mean-field equations: nonlinear integral equations for the populations of the three states. We analyze the stability of their steady solutions. Collective oscillations are shown to persist in a large parameter region beyond supercritical and subcritical Hopf bifurcations. We compare the results with simulations of discrete units as well as of coupled FitzHugh-Nagumo systems.
Keywords:Action Potentials, Biological Clocks, Computer Simulation, Markov Chains, Neurological Models, Statistical Models, Nerve Net, Neurons, Animals
Source:Physical Review E
ISSN:1539-3755
Publisher:American Physical Society (U.S.A.)
Volume:76
Number:1 Pt 1
Page Range:011118
Date:24 July 2007
Official Publication:https://doi.org/10.1103/PhysRevE.76.011118
PubMed:View item in PubMed

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