Diffusion-driven instability in a predator-prey system with time-varying diffusivities

We consider an ecological model by Levin and Segel (1976) for predator-prey planktonic species, which consists of two reaction-diffusion equations, and extend it to plankton populations with time-varying diffusivities. The local stability of uniform equilibria is examined both analytically and numerically. It is found that diffusive instability is less likely to occur in systems with time-varying diffusivity than those with constant diffusivity. Contribution No. 803 of the Marine Sciences Research Center, State University of New York, Stony Brook Supported by the Danish Science Research Council (Grant nos. 11-7128, 11-8321), the Danish Research Academy (Grant nos. E-880011, V-890085) and a Travel Grant for Mathematicians (Rejselegat for Matematikere) Supported by Hudson River Foundation, Grant no. 01488AO37