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

• Published in: Computers & mathematics with applications (1987) Vol. 64; no. 10; pp. 3329 - 3339
• Main Authors: Moaddy, K., Radwan, A.G., Salama, K.N., Momani, S., Hashim, I.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-11-2012
• Subjects: Chaotic synchronization; Derivatives; Fractional differential equation; Neuron system; Non-standard finite deference scheme; Fractional differential equation; Neuron system; Chaotic synchronization; Non-standard finite deference scheme
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2012.01.005

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.