Annihilation of Bumps in Two-Population Neural Field Model Under the Influence of Gaussian External Input

Abstract

In this work, we have examined the impact of Gaussian-type spatio-temporal external input on annihilation of self-managed activity states (bumps) in a Wilson-Cowan type two- population neural field model. These activity states plays the role of the intellectual framework with a restricted limit that can hold information known as working memory in the prefrontal cortex. The effect of various parameters engaged with the external input on annihilation of these persistent activity states is researched in detail. This very choice of Gaussian-type spatio-temporal external input is quite near the nature as seen by Roth et al. [4]. In this work eraser mechanism is used to annihilate the spatially symmetric solutions. If there is an activity in the network, inhibitory external input with no excitatory part in the external input can kill the activity. In the whole of our investigation, the prominent thing is Gaussian-type function which yields quite better findings in spite of three sided (triangular function) used by Yousaf et al. [5]. It is additionally discovered that the relative inhibition time constant serves as a pivotal role in annihilation of the activity. Runge-Kutta fourth order method has been used for mathematical simulations of this work.