Analysis of dynamic properties on forest restoration-population pressure model

On the basis of logistic models of forest restoration, we consider the influence of population pressure on forest restoration and establish a reaction diffusion model with Holling Ⅱ functional responses. We study this reaction diffusion model under Dirichlet boundary conditions and obtain a positive equilibrium. In the square region, we analyze the existence of Turing instability and Hopf bifurcation near this point. The square patterns and mixed patterns are obtained when steady-state bifurcation occurs, the hyperhexagonal patterns appears in Hopf bifurcation.