In our numerical simulation, a modified Fitzhugh-Nagumo model, which was used to describe the excitable and/or oscillatory media under appropriate parameters, was investigated.

Existence of periodic solutions for p-Laplacian differential equation with Nagumo condition;

By using Upper and Lower solutions method,Leray-Schauder degree theory and Differential inequality method,we establish the existence and uniqueness theorems for a kind of nth-order nonlinear two-point boundary value problems with weaker Nagumo condition, and we give an example to demmonstrate our results.

The dynamical behavior of discrete Nagumo equation is studied, and it is proved by using anti\| integrability method that there exist the breather solutions in the discrete system.