Two Population Neural Field Model With Constant External Input

Abstract

In this work, We have study the two-population neural field Model under the effect of constant external inputs. Earlier, Blomquist et al.[1] investigated the stationary symmetric solution of two population model with no external input.They found that Amari stability analysis and linearized stability analysis produces same results. Later on Yousaf et al. [2] investigated the same model under the influence of spatial dependent external input and proved that the Amari technique and linearized stability technique does not produce same results. They also investigate the number of bumps as a function of amplitude parameter of external input and found at most four bump pairs. In our research work, We have to explore the two population neural field model under the effect of constant external input on bump solutions. We further, have to investigate the stability properties of stationary symmetric solutions by using two approaches (i) Amari approach (ii) standard linearized approach. Numerically, We will investigate the number of bumps as a function of width and amplitude parameter of external input