Eventual dissipativeness and synchronization of nonlinearly coupled dynamical network of Hindmarsh-Rose neurons

Chun Hsien Li, Suh Yuh Yang

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13 Scopus citations

Abstract

In this paper, we study the asymptotic collective behavior of nonlinearly coupled dynamical network of Hindmarsh-Rose neurons, where the neurons are asymmetrically interconnected through a sigmoidal coupling function. We first show that the nonlinearly coupled dynamical network with a certain asymmetric connection topology is eventually dissipative and hence all solutions are eventually bounded. Furthermore, under some mild conditions on the system parameters, we derive an eigenvalue-related criterion that ensures the nonlinearly coupled dynamical network to be globally exponentially synchronized. Numerical experiments for the modular network of Hindmarsh-Rose neurons with or without the small-world property are given to demonstrate the theoretical results.

Original languageEnglish
Pages (from-to)6631-6644
Number of pages14
JournalApplied Mathematical Modelling
Volume39
Issue number21
DOIs
StatePublished - 1 Nov 2015

Keywords

  • Coupled dynamical network
  • Eventual dissipativeness
  • Global synchronization
  • Hindmarsh-Rose neuron
  • Lyapunov function
  • Modular network

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