A note on a diffusive predator-prey model and its steady-state system |
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Authors: | Rui Peng Ming Xin Wang Guo Ying Yang |
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Institution: | (1) Division of Mathematics, University of Dundee, Dundee, DD1 4HN, UK;(2) College of Life Sciences, University of Dundee, Dundee, DD1 4HN, UK |
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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. |
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Keywords: | a diffusive predator-prey model steady states global stability a priori-estimates non-existence |
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