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

Zeeshan Afzal,Naima Amin,Chahn Yong Jung,Muhammad Yousaf Bhatti,Asif Mushtaq

doi:10.1109/access.2019.2933263

Abstract

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.

Highlights

The human brain is stimulating system contains billions of neurons
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)
We have investigated the phenomenon of annihilation of the activity in network using spatio-temporal external input with α-type temporal part

Summary

INTRODUCTION

The human brain is stimulating system contains billions of neurons (nerve cells). The average human brain weighs about 1.2–1.4 kilograms and it is the most complex organ in the human body. Z. Afzal et al.: Effect of Alpha-Type External Input on Annihilation of Self-Sustained Activity in a Two-Population Neural Field Model of coherent structures for different modeling approaches is investigated in many studies [3], [6], [7], [9]–[14]. This work is an extension of the work done by Yousaf et al [19] where they investigated the bump solution of two-population neural field model with spatio-temporal external input They formulated the general necessary condition for emergence of persistent activity states. The effect of external input on 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 by Afzal et al [20]. We prove that the solution of initial value problem (10) are uniformly bounded provided both the initial conditions and the external input functions are bounded and continuous

BOUNDEDNESS

RESULTS

CONCLUSION AND DISCUSSIONS