Synchronization of Morris-Lecar mathematical models of neural activity

Abstract

This work is devoted to the problem of synchronization of two Morris-Lecar neuron models. The Morris-Lecar model is a second-order system of differential equations, which describes an uneasy relationship between the membrane potential and the activation of ion channels inside the membrane. Synchronization, which is a state of a network when models begin to act similarly in some sense, of such models is interesting not only from a mathematical point of view, but also from a biological one, because synchronous activity plays a very important role in brain functioning. The speed gradient algorithm, which is a continuous version of gradient algorithms, was applied to solve this problem. The algorithm of coupling strength control was obtained. It ensures the achievement of the control goal. The MATLAB modelling demonstrated the correctness of the obtained result and fast convergence rate of corresponding models' variables to each other.