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

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.

Citation
Moaddy, K., Radwan, A. G., Salama, K. N., Momani, S., & Hashim, I. (2012). The fractional-order modeling and synchronization of electrically coupled neuron systems. Computers & Mathematics with Applications, 64(10), 3329–3339. doi:10.1016/j.camwa.2012.01.005

Publisher
Elsevier BV

Journal
Computers & Mathematics with Applications

DOI
10.1016/j.camwa.2012.01.005

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