Abstract: We considered the dynamic bifurcation  problem of a class of cross-reaction-diffusion models with Holling-Ⅱ functional response function under non-homogeneous Dirichlet boundary conditions. Firstly, the critical crossing conditions for the corresponding linearization problem eigenvalues were obtained by using the spectral analysis theory. Secondly,  the environmental carrying coefficient was selected as the bifurcation parameter, the analytical expression of the dynamic transition type and bifurcation solution of the system was obtained by using the center manifold reduction and the dynamic bifurcation theory. Finally, by using the finite difference method, the pattern change patterns of the system were given under  different parameter conditions.

Key words: reaction-diffusion model, eigenvalue analysis, dynamic transition, numerical simulation