Numerical Simulation On Existence And Uniqueness Of Traveling Wave Solutions Of Integral Differential Equations Arising From Neuronal Networks

In this paper, the existence and uniqueness of traveling wave solutions of integral differential equations:are discussed. The theorem and proof of existence and uniqueness of traveling wave solutions are given in [l],but its proof is incomplete enough. Via the wrong conclusion in [1] is pointed out by paper [1], equations are put into the autonomous system, and the cases of the fixed points are analyzed in the vector field, further, existence and uniqueness of traveling wave solutions are described in various cases. The using of Matlab in this paper based on the paper [3], then the portraits in phase plane are drawn in the autonomous system. At first, the numerical simulations about existence of traveling wave solutions and unique wave speed are given while w=0.Secondly, the numerical simulations about cases of two, three and six fixed points are pictured. At last, existence and uniqueness of traveling wave solutions is illustrated in different case.