Construction of new numerical scheme based on implicit method for two-population neural field model.

Abstract

The brain is the most complex organ of the human body. Neuron is the basic unit of brain. Signals are transmitted from one part of the brain to the other parts in the form of impulses. This mechanism is translated by different mathematical models. In this work we have explored the two-population neural field (TPNF) model which describes the activity of excitatory and inhibitory populations of neurons. This model is explored without external inputs, with spatial and with spatio-temporal external inputs. For numerical study of the model explicit Runge-Kutta method of order four is used. We developed a new numerical scheme based on implicit RK4 method and have studied the evolution of the solutions of the model for no external inputs and with external inputs.