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UFN, 2002, Volume 172, Number 1, Pages 31–66 (Mi ufn1972)  

This article is cited in 33 scientific papers (total in 33 papers)


Spatio-temporal pattern formation, fractals, and chaos in conceptual ecological models as applied to coupled plankton-fish dynamics

A. B. Medvinskiia, S. V. Petrovskiib, I. A. Tikhonovaa, D. A. Tikhonova, B.-L. Lic, E. Venturinod, H. Malchowe, G. R. Ivanitskiia

a Institute for Theoretical and Experimental Biophysics, Russian Academy of Sciences
b P. P. Shirshov institute of Oceanology of RAS
c Department of Biology, University of New Mexico
d Dipartimento di Matematica, Politecnico di Torino
e Institute of Environmental Systems Research, University of Osnabrück

Abstract: The current turn-of-the-century period witnesses the intensive use of the bioproducts of the World Ocean while at the same time calling for precautions to preserve its ecological stability. This requires that biophysical processes in aquatic systems be comprehensively explored and new methods for monitoring their dynamics be developed. While aquatic and terrestrial ecosystems have much in common in terms of their mathematical description, there are essential differences between them. For example, the mobility of oceanic plankton is mainly controlled by diffusion processes, whereas terrestrial organisms naturally enough obey totally different laws. This paper is focused on the processes underlying the dynamics of spatially inhomogeneous plankton communities. We demonstrate that conceptual reaction-diffusion mathematical models are an appropriate tool for investigating both complex spatio-temporal plankton dynamics and the fractal properties of planktivorous fish school walks.


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English version:
Physics–Uspekhi, 2002, 45:1, 27–57

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PACS: 05.45.-a, 92.10.-c, 92.20.Rb
Received: March 26, 2001

Citation: A. B. Medvinskii, S. V. Petrovskii, I. A. Tikhonova, D. A. Tikhonov, B.-L. Li, E. Venturino, H. Malchow, G. R. Ivanitskii, “Spatio-temporal pattern formation, fractals, and chaos in conceptual ecological models as applied to coupled plankton-fish dynamics”, UFN, 172:1 (2002), 31–66; Phys. Usp., 45:1 (2002), 27–57

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    4. Martin A., “Phytoplankton Patchiness: the Role of Lateral Stirring and Mixing”, Prog. Oceanogr., 57:2 (2003), 125–174  crossref  adsnasa  isi
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    7. Yu. V. Bibik, S. P. Popov, D. A. Sarancha, “Numerical solution of the Bogoyavlenskii kinetic equation and the Lotka–Volterra system with diffusion”, Comput. Math. Math. Phys., 44:5 (2004), 856–867  mathnet  mathscinet  zmath
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    10. Grieco L., Tremblay L., Zambianchi E., “A Hybrid Approach to Transport Processes in the Gulf of Naples: an Application to Phytoplankton and Zooplankton Population Dynamics”, Cont. Shelf Res., 25:5-6 (2005), 711–728  crossref  adsnasa  isi  elib  scopus
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