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Chaotic synchronization in ensembles of coupled neurons modeled by the FitzHugh-Rinzel system

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Abstract

We consider various networks of diffusively coupled identical neurons modeled by a system of FitzHugh-Rinzel coupled differential equations. The mathematical model of a solitary nerve cell is analyzed theoretically and numerically. Regions corresponding to the qualitatively different behavior of a neuron are separated in the parameter space of the system. We present synchronization conditions in a network in which the central element modeling the pacemaking neuron is linked to the group of uncoupled neurons (star configuration). Within the framework of the connection graph stability method [1], which allows us to determine the character of variation in the threshold values of the coupling strengths sufficient for establishing the complete-synchronization regime, we study the influence of the network structure on the synchronization thresholds in different ensembles. In particular, we consider a configuration in the form of diffusively coupled stars structures.

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Authors and Affiliations

  1. Volga State Academy of Water Transport, Nizhny Novgorod, Russia

    V. N. Belykh & E. V. Pankratova

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  1. V. N. Belykh
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  2. E. V. Pankratova
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 11, pp. 1002–1014, November 2006.

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Belykh, V.N., Pankratova, E.V. Chaotic synchronization in ensembles of coupled neurons modeled by the FitzHugh-Rinzel system. Radiophys Quantum Electron 49, 910–921 (2006). https://doi.org/10.1007/s11141-006-0124-z

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  • DOI: https://doi.org/10.1007/s11141-006-0124-z

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