Emergence of Persistent Activity States in a Two-Population Neural Field Model for Smooth $\alpha$ -Type External Input

We investigate the emergence of localized activity states, so-called bumps in Wilson-Cowan type two-population neural field model under the influence of transient spatio-temporal external input with smooth α-type temporal function. This two-population model is composed of two coupled nonlinear differential equations derived for the dynamics of spatially localized populations of both excitatory and inhibitory model neurons. The model with no external input corresponds to at most two bump pair solutions. Such a system can be interpreted as a minimal cortical model for short term working memory, that is the ability of the brain to actively hold stimulus-related information for some seconds in short term memory and discards once it becomes irrelevant Initially, if there is no activity in the system, persistent activity state can be evoked by switching on a suitable transient excitatory external input. This activity remains stable even though external input is switched off. The effect of external input on the emergence of bumps for different spatial and smooth 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., relative inhibition time constant, total duration, and the amplitude 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 Yousaf et al. showing that the present choice of temporal function in the external input is more effective and more close to natural behavior.