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

Authors:
K. Moaddy;A. G. Radwan;K. N. Salama;S. Momani;I. Hashim
Affiliations:
School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600, UKM Bangi, Selangor, Malaysia;Electrical Engineering Department, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia and Department of Engineering Mathematics Faculty of Engineering, Cairo Universi ...;Electrical Engineering Department, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia;Department of Mathematics, The University of Jordan, Amman 11942, Jordan;School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600, UKM Bangi, Selangor, Malaysia
Venue:
Computers & Mathematics with Applications
Year:
2012

Citing 4
Cited 1

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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 Grunwald-Letnikov discretization process which is easily implemented and reliably accurate.