Maximal attractor, stability, and persistence for prey-predator model with saturation

By the comparison theorem and linearization, the stability of steady-state solutions for prey-predator model with saturation is discussed, and conditions imposed on parameters for the stability are given. The estimate of linear semigroup and the general theory of uniform persistence are used to prove the existence of maximal attractor in [C0(\̄gW)]2 and the uniform persistence.