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Spatiotemporal pattern formation in a diffusive predator-prey system: An analytical approach. (English) Zbl 1181.35022
Summary: We propose and analyse a mathematical model to study the mathematical aspect of the reaction diffusion pattern formation mechanism in a predator-prey system. An attempt is made to provide an analytical explanation for understanding plankton patchiness in a minimal model of an aquatic ecosystem consisting of phytoplankton, zooplankton, fish and nutrient. The reaction diffusion model system exhibits spatiotemporal chaos causing plankton patchiness in a marine system. Our analytical findings, supported by the results of numerical experiments, suggest that an unstable diffusive system can be made stable by increasing diffusivity constant to a sufficiently large value. It is also observed that the solution of the system converges to its equilibrium faster in the case of two-dimensional diffusion in comparison to the one-dimensional diffusion. The ideas contained in the present paper may provide a better understanding of the pattern formation in a marine ecosystem.

35B36Pattern formation in solutions of PDE
35B35Stability of solutions of PDE
92C15Developmental biology, pattern formation
35K57Reaction-diffusion equations
Full Text: DOI
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