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Zbl 1001.92050
Medvinsky, Alexander B.; Petrovskii, Sergei V.; Tikhonova, Irene A.; Malchow, Horst; Li, Bai-Lian
Spatiotemporal complexity of plankton and fish dynamics. (English)
[J] SIAM Rev. 44, No.3, 311-370 (2002). ISSN 0036-1445; ISSN 1095-7200/e

Summary: Nonlinear dynamics and chaotic and complex systems constitute some of the most fascinating developments of late twentieth century mathematics and physics. The implications have changed our understanding of important phenomena in almost every field of science, including biology and ecology. This article investigates complexity and chaos in the spatiotemporal dynamics of aquatic ecosystems. The dynamics of these biological communities exhibit an interplay between processes acting on a scale from hundreds of meters to kilometers, controlled by biology, and processes acting on a scale from dozens to hundreds of kilometers, dominated by the heterogeneity of hydrophysical fields. We focus on how biological processes affect spatiotemporal pattern formation. Our results show that modeling by reaction-diffusion equations is an appropriate tool for investigating fundamental mechanisms of complex spatiotemporal plankton dynamics, fractal properties of planktivorous fish school movements, and their interrelationships.

MSC 2000:: *92D40 Ecology
37N25 Dynamical systems in biology
82C41 Dynamics of random walks, etc.
35K57 Reaction-diffusion equations

Keywords: chaos; order; scaling; aquatic ecosystems; predator-prey interaction; modeling

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