Radiophysics and Quantum Electronics

, Volume 49, Issue 11, pp 910–921 | Cite as

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

  • V. N. Belykh
  • E. V. Pankratova


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.


Lyapunov Function Coupling Strength Network Element Coupling Matrix Complete Synchronization 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. N. Belykh
    • 1
  • E. V. Pankratova
    • 1
  1. 1.Volga State Academy of Water TransportNizhny NovgorodRussia

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