Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 196, Issue 1-2, Pages 172-192Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physd.2004.05.007
Keywords
elliptic system; prey-predator model; diffusion; stationary patterns
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We study a reaction diffusion system arising from a three-species prey-predator model with prey-dependent and ratio-dependent functional responses. The main aim of this paper is to study the global existence and bifurcation of non-constant positive steady-states. In particular, we will show that even though the unique positive constant steady-state is stable for the ODE dynamics, non-constant positive steady-states exist for the reaction diffusion system. This demonstrates that stationary patterns arise as a result of diffusion. (C) 2004 Elsevier B.V. All rights reserved.
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