Abstract: This paper deals with a prey-predator model with the third boundary value to the prey. First, the authors obtain that the model has positive stationary solutions if and only if a>mb+d₁λ₁. Secondly, the authors prove the local
stability and uniqueness of its positive stationary solution. Thirdly, the authors study the change of existence of its positive stationary solution when the coefficients of its diffusion terms approach infinity.

Key words: Prey-predator model, Existence of positive stationary solutions,
Degree theory, Bifurcation theory, Stability, Uniqueness