Two-Bump Solutions in the Two-Population Neural Field Model

Abstract

Two-Population model represents excitatory and inhibitory activity levels in the brain in cortex. Their stationary symmetric solution of population is named as bump. The bump serves as a working memory in the brain. There are two types of bump solutions. So one is a single bump solution and other is double, its solution is the form of pairs. This form presents one bump pairs and two or double bump pairs. So far earlier, it has been investigated that lots of work has been done on single bump pair solutions. Now our target is to investigate the emergence of double bump pair oblige two bump pair solutions. We investigated different parameters to find the existence of double bump pair solutions. We further investigated the existence of a double bump pair solu- tion and by using Spatial Independent no external input and with external input as well. We concluded that there does not exist any double bump pair solution in the two-population neural field model(TPNFM). Therefore we have the motive of this thesis to investigate the existence of double or two bump pair solutions in TPNFM.