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

K. Moaddy, A. G. Radwan, K. N. Salama, S. Momani, Ishak Hashim

Research output: Contribution to journalArticle

88 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)3329-3339
Number of pages11
JournalComputers and Mathematics with Applications
Volume64
Issue number10
DOIs
Publication statusPublished - Nov 2012

Fingerprint

Fractional Order
Neurons
Neuron
Synchronization
Modeling
Nonstandard Finite Difference Schemes
Gap Junction
Chaotic Synchronization
Long Memory
State Equation
Fractional Derivative
Cables
Numerical Techniques
Cable
Derivatives
Data storage equipment
Discretization
Networks (circuits)
Generalise
Integer

Keywords

  • Chaotic synchronization
  • Fractional differential equation
  • Neuron system
  • Non-standard finite deference scheme

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Modelling and Simulation
  • Computational Mathematics

Cite this

The fractional-order modeling and synchronization of electrically coupled neuron systems. / Moaddy, K.; Radwan, A. G.; Salama, K. N.; Momani, S.; Hashim, Ishak.

In: Computers and Mathematics with Applications, Vol. 64, No. 10, 11.2012, p. 3329-3339.

Research output: Contribution to journalArticle

Moaddy, K. ; Radwan, A. G. ; Salama, K. N. ; Momani, S. ; Hashim, Ishak. / The fractional-order modeling and synchronization of electrically coupled neuron systems. In: Computers and Mathematics with Applications. 2012 ; Vol. 64, No. 10. pp. 3329-3339.
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