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Zbl 1181.35022
Dubey, Balram; Kumari, Nitu; Upadhyay, Ranjit Kumar
Spatiotemporal pattern formation in a diffusive predator-prey system: An analytical approach. (English)
[J] J. Appl. Math. Comput. 31, No. 1-2, 413-432 (2009). ISSN 1598-5865; ISSN 1865-2085/e

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.

MSC 2000:: *35B36
35B35 Stability of solutions of PDE
92C15 Developmental biology, etc.
35K57 Reaction-diffusion equations

Keywords: prey-predator system; reaction-diffusion equations; marine ecosystem; chaos; spatiotemporal pattern

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Zentralblatt MATH Berlin [Germany]