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.
Moaddy K., Radwan A.G., Salama K.N., Momani S., Hashim I.
Chaotic synchronization; Fractional differential equation; Neuron system; Non-standard finite deference scheme
Computers and Mathematics with Applications, Vol. 64, PP. 3329 to 3339, Doi: 10.1016/j.camwa.2012.01.005