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A note on a diffusive predator-prey model and its steady-state system
Authors:Rui Peng  Ming Xin Wang  Guo Ying Yang
Institution:(1) Division of Mathematics, University of Dundee, Dundee, DD1 4HN, UK;(2) College of Life Sciences, University of Dundee, Dundee, DD1 4HN, UK
Abstract:In this note, a diffusive predator-prey model subject to the homogeneous Neumann boundary condition is investigated and some qualitative analysis of solutions to this reaction-diffusion system and its corresponding steady-state problem is presented. In particular, by use of a Lyapunov function, the global stability of the constant positive steady state is discussed. For the associated steady state problem, a priori estimates for positive steady states are derived and some non-existence results for non-constant positive steady states are also established when one of the diffusion rates is large enough. Consequently, our results extend and complement the existing ones on this model.
Keywords:a diffusive predator-prey model  steady states  global stability  a priori-estimates  non-existence
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