Emergence of Bumps for Piece Wise Defined External Input in a Two-Population Neural Field Model

Abstract

In this research, we have studied the appearance of bump solutions (localized activity states) in a two-population neural field model for the temporary external input that depends on space and time with piece wise define temporal part. The same model has been investigated by Blomquist et al [2] with no external input and later on by Yousaf et al with spatial and spatio temporal dependent external inputs [3,5]. Zeshan et al [4] investigated the same model for more realistic approach for temporal function (𝛼-type function) in the spatio external input. In present study, we explored the appearance of bump solutions (persistent localized activity states) for more detailed temporal part (piece wise defined) in the spatio external input of for the above said model. The effect of external input on appearance of bumps for different spatial, piece wise 𝛼-type temporal functions of external input is investigated and found that certain parameters play a key role in the generation of persistent activity states in the network e.g. 𝜏(relative inhibition time constant), 𝑇𝑒 (total duration), 𝐶𝑒(amplitude), 𝑡1(inclination peak time) and 𝑡2 (Peak time duration) of external input. It is found that the minimum values of the amplitude and active time to evoke the activity in the network is smaller than those observed in prior studies. These results show that the present choice of temporal functions in the external input is more effective and efficient