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

A.B. Medvinskii^a, S.V. Petrovskii^b, I.A. Tikhonova^a, D.A. Tikhonov^a, B.L. Li^c, E. Venturino^d, H. Malchow^e, G.R. Ivanitskii^a
^aInstitute for Theoretical and Experimental Biophysics, Russian Academy of Sciences, Institutskaya str. 3, Pushchino, Moscow Region, 142290, Russian Federation
^bP.P. Shirshov Institute of Oceanology, Russian Academy of Sciences, ul. Krasikova 23, Moscow, 117218, Russian Federation
^cDepartment of Biology, The University of New Mexico, 167A Castetter Hall, Albuquerque, New Mexico, 87131-1091, USA
^dDipartimento di Matematica, Corso Duca degli Abruzzi, 24, Politecnico di Torino, Torino, 10129, Italy
^eInstitute of Environmental Systems Research, University of Osnabrueck, Artilleriestr. 34, Osnabrueck, D-49069, Germany

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.

PACS: 05.45.−a, 92.10.−c, 92.20.Rb (all)
DOI: 10.1070/PU2002v045n01ABEH000980
URL: https://ufn.ru/en/articles/2002/1/b/
Web of Science

000175529500002
Citation: Medvinskii A B, Petrovskii S V, Tikhonova I A, Tikhonov D A, Li B L, Venturino E, Malchow H, Ivanitskii G R "Spatio-temporal pattern formation, fractals, and chaos in conceptual ecological models as applied to coupled plankton-fish dynamics" Phys. Usp. 45 27–57 (2002)

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Оригинал: Медвинский А Б, Петровский С В, Тихонова И А, Тихонов Д А, Ли Б Л, Вентурино Э, Мальхё Х, Иваницкий Г Р «Формирование пространственно-временных структур, фракталы и хаос в концептуальных экологических моделях на примере динамики взаимодействующих популяций планктона и рыбы» УФН 172 31–66 (2002); DOI: 10.3367/UFNr.0172.200201b.0031