Dynamics of a diffusive predator-prey model: the effect of conversion   rate
  A general diffusive predator-prey model is investigated in this paper. We prove the global attractivity of constant equilibria when the conversion rate is small, and the non-existence of non-constant positive steady states when the conversion rate is large. The results are applied to several predator-prey models and give some ranges of parameters where complex pattern formation cannot occur. 
Shanshan Chen and Junjie Wei and Jianhui Zhang
math.DS