Analysis of a network of electrically coupled neurons in fractional domain

Synaptic signal transduction between nerve cells is mediated by electrical coupling in biological systems, implying the dynamic behavior of each cell in such a cluster of functionally similar neurons is inevitably influenced by the electrical properties of the whole network. This study demonstrates that when cell membranes are modeled after fractional order circuit elements, analytical solutions to the network equations can be found that describe the dynamic responses of any given cell to a single stimulus in greater and more accurate detail. Transfer function and the driving point impedance for this circuit network are derived in the fractional domain based on the application of the transmission matrices concept. Furthermore, necessary MATLAB simulations are performed on the network and are included as a numerical example.