Effect of Alpha-Type External Input on Annihilation of Self-Sustained Activity in a Two Population Neural Field Model

In the present work, we investigate the annihilation of persistent localized activity states (bumps) in a Wilson-Cowan type two-population neural field model in response to α-type spatio-temporal external input. These activity states serves as working memory in the prefrontal cortex. The impact of different parameters involved in the external input on annihilation of these persistent activity states is investigated in detail. The α-type temporal function in the external input is closer to natural phenomenon as observed in Roth et. al. (Nature Neuroscience, vol. 19 (2016), 229-307). Two types of eraser mechanism are used in this work to annihilate the spatially symmetric solutions. Initially, if there is an activity in the network, inhibitory external input with no excitatory part and over excitation with no inhibition in the external input can kill the activity. Our results show that the annihilation of persistent activity states using α-type temporal function in the external input is more roubust and more efficient as compare to triangular one as used by Yousaf et al. (Neural networks.,vol. 46 (2013), pp. 75-90). It is also found that the relative inhibition time constant plays a crucial role in annihilation of the activity. Runge-Kutta fourth order method has been employed for numerical simulations of this work.