Stability Analysis Of Two Classes Of Prey-Predator Model

In this paper, we consider the Turing instability of two classes cross diffusion models with three species where ?0, ?1, ?2, ?2, ?,?0,?1,m1, m2, r, ? and di(i= 1,2,3,4) are positive constant, ? is a bounded domain in Rn.Through the linear analysis, the unique positive equilibrium point E*(u1*, u2*,u3*) of (1) (or (2))corresponding ODE model and semilinear reaction diffusion model is stable under certain conditions. But under the same conditions, when the diffusion coefficient is sufficiently large, E*(u1*, u2* u3*) is unstable equilibrium point of (1) (or (2)), it means that the Turing instability occurs.