Effects of Spatial Parts of the External Input on Bumps in the Two-Population Neural Field Model

Abstract

The Two-Population Neural Field Model (TPNF) of Wilson-Cowan type represents excitatory and inhibitory activity levels in the brain. The stationary and symmetric solution of this model is Bump pair which serves as working memory/self-sustained activity in the brain. Therefore, it is very important to investigate the appearance and disappearance of these activities. There exist two Bumps Pair solution (i.e. one narrow and other named as broad bump pair) for the case of without external input. The narrow bump pair is not stable for all values of τ (Relative inhibition time constant). The Broad Bump pair is stable for the suitable value (small and moderate value) of the τ. The impact of spatio-temporal external input on appearance of bumps for different temporal part has already been investigated in detail but the spatial part of the external input is equally important and has not been investigated that much. We have investigated the impacts of spatiotemporal external input on appearance bump solutions of the TPNF Model with a focus on spatial parts of the external input. We considered four possible functions for this purpose and found that the broad bump choice as a spatial function in the external input is the most suitable to evoke the activity in the network.