The fractional-order modeling and synchronization of electrically coupled neuron systems

K. Moaddy, Ahmed G. Radwan, Khaled N. Salama, Shaher M. Momani, Ishak Hashim

Research output: Contribution to journalArticlepeer-review

103 Scopus citations

Abstract

In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald-Letnikov discretization process which is easily implemented and reliably accurate. © 2011 Elsevier Ltd. All rights reserved.
Original languageEnglish (US)
Pages (from-to)3329-3339
Number of pages11
JournalComputers & Mathematics with Applications
Volume64
Issue number10
DOIs
StatePublished - Nov 2012

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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