Mutually Inhibiting Neural Networks with Second Order Neuronal Activities

In this paper, we propose new mathematical second-order model to replicate neuronal activities of mutually inhabiting neural networks. The inclusion of second order differential equations captures complex neural behaviour more accurately instead of first order differential equations. A non-autonomous system of coupled second-order differential equation is proposed in this paper to govern the neuronal dynamics of a neural network of N neurons. Simulation results of single neuron and network of two neurons are shown graphically. The results provide insights into oscillatory patterns, stable states, and variation in the behaviour of neurons with respect to time. It is found that the neural system exhibits oscillatory response that can be used to govern various motion gaits and cyclic activities.