Traveling Wave Of A Neural Field System With Excitatory And Inhibitory Neurons

In this paper, we consider a homogenized two-population neural field model of excitatory and inhibitory neurons with a periodically modulated weight distribution ω(x,y)=ω(x-y)[1+K(y/ε)], where2πε is the period of the modulation with K(x)=K(x+2π) for all x and y/ε is a slow spatial variable for very small ε. Assume that the unperturbed network has a constant input, and the presynaptic scaling factors are constants, we prove the existence of traveling wave and give an analysis of the corresponding wave speed.In chapter two we work with the exponential weight distribution Φ(x)=1/2e-|x|in the neural field homogenized model of excitatory and inhibitory neurons. According to the properties of weight distribution and the monotonicity of traveling front solu-tion, we give the explicit formulas of the traveling front solution which connects two stationary states and prove the existence of the corresponding wave speed.In chapter three we work with the the Gaussian distributions of excitatory and inhibitory neural connections in the neural field homogenized model of excitatory and inhibitory neurons. We give the explicit formulas of the traveling front solution which connects two stationary states and prove the existence of the corresponding wave speed.In chapter four we give some discussions on the neural field homogenized model of excitatory and inhibitory neurons and give some problems in the future work.