Annihilation of Bumps for Piecewise Defined External Input in a Two-Population Neural field Model

Abstract

In this Research Proposal, we have to analyze the Annihilation mechanism of persistent localized activity states (bumps) in response to transient Spatio-temporal external input with piecewise temporal function in two-population neural field model of the Wilson-Cowan type [1]. Blomquist et al.[2] explored the bump solutions of two- population neural field models with no external input. Two separate methodologies are utilized to investigate the stability of bumps, the Amari methodology and direct linearization process stability. It was shown both mathematically and numerically that Ammari and full linearized stability produces same results. Directly after, the same model was investigated by spatial dependent and Spatio- temporal external input, by Yousaf .et. al [3, 4]. Afzal. Z [5, 6] studied the bump solution of a two-population neural field model with a smooth $alpha$-type temporal function under the effect of transitory Spatio-temporal external input. For a detailed exploration of the effects of different parameters of external input, it was further classified into amplitude, spatial, and temporal parts. We are investigating the annihilation of localized activity states (bumps) in response to transient Spatio- temporal external input with piecewise temporal function in a two-population neural field model of the Wilson-Cowan type. In the 4th chapter, we will present the conclusion of our thesis. In the 5th chapter, we will present the references of our thesis.