In this paper,the neural localization dynamics behavior of FN (fizhughnagumo) model under boundary conditions is studied.The theoretical study is carried out on the FN model with diffusion,and the normal differential equation with boundary is obtained by the method of discrete Laplace operator,then the specific effect of boundary conditions on the system is analyzed.Also,the different parameter of the mixed boundary is studied and the relationship between a mixed boundary value and matrix spectral is obtained.Finally,the results are verified by numerical simulation,the new pattern mechanism of FN model about grid cell is proposed,and the regulation method of pattern formation is present.