Reviews of topical problems

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

 a,  b,  a,  a,  c,  d,  e,  a
a Institute for Theoretical and Experimental Biophysics, Russian Academy of Sciences, Institutskaya str. 3, Pushchino, Moscow Region, 142290, Russian Federation
b P.P. Shirshov Institute of Oceanology, Russian Academy of Sciences, ul. Krasikova 23, Moscow, 117218, Russian Federation
c Department of Biology, The University of New Mexico, 167A Castetter Hall, Albuquerque, New Mexico, 87131-1091, USA
d Dipartimento di Matematica, Corso Duca degli Abruzzi, 24, Politecnico di Torino, Torino, 10129, Italy
e Institute 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.

Text can be downloaded in Russian. English translation is available on IOP Science.
PACS: 05.45.−a, 92.10.−c, 92.20.Rb (all)
DOI: 10.1070/PU2002v045n01ABEH000980
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

References (268) Cited by (25) ↓ Similar articles (20)

  1. Tyutyunov Yu V, Zagrebneva A D et al Advanced Mathematical Methods in Biosciences and Applications STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health Chapter 10 (2019) p. 221
  2. Giricheva E Nonlinear Dyn 95 875 (2019)
  3. Il’ichev V G, Il’icheva O A BIOPHYSICS 63 274 (2018)
  4. (Proceedings of the International Conference "Mathematical Biology and Bioinformatics") Vol. Proceedings of the International Conference "Mathematical Biology and Bioinformatics"Spatial-temporal structures in the active predator-passive prey modelA.D.ZagrebnevaV.N.Govorukhin7 (2018)
  5. Medvinsky A B, Nurieva N I et al BIOPHYSICS 62 92 (2017)
  6. Bel’chinskaya L I, Khodosova N A et al Prot Met Phys Chem Surf 53 793 (2017)
  7. Giricheva E E CRM 8 549 (2016)
  8. Zemskov E P Uspekhi Fizicheskikh Nauk 184 1149 (2014) [Zemskov E P Phys.-Usp. 57 1035 (2014)]
  9. Bobyrev A E, Burmensky V A et al BIOPHYSICS 58 245 (2013)
  10. Roelke D L, Eldridge P M Ecological Modelling 221 1017 (2010)
  11. Medvinsky A B, Rusakov A V et al BIOPHYSICS 54 90 (2009)
  12. Kulagina T P, Smirnov L P Russ. J. Phys. Chem. B 3 910 (2009)
  13. ISHIKAWA M AECE 8 2 (2008)
  14. Medvinsky A B, Gonik M M et al Ecological Complexity 4 201 (2007)
  15. Gonik M M, Bobyrev A E et al BIOPHYSICS 52 445 (2007)
  16. Medvinsky A B, Kriksunov E A et al BIOPHYSICS 51 309 (2006)
  17. Medvinsky A B BIOPHYSICS 51 908 (2006)
  18. Trott M The Mathematica GuideBook for Numerics Chapter 1 (2006) p. 1
  19. Medvinsky A B, Gonik M M et al Journal Of Theoretical Biology 242 539 (2006)
  20. Grieco L, Tremblay L -B, Zambianchi E Continental Shelf Research 25 711 (2005)
  21. Vanag V K Uspekhi Fizicheskikh Nauk 174 991 (2004)
  22. Vysikailo P I J. Exp. Theor. Phys. 98 936 (2004)
  23. Purtov P A Appl. Magn. Reson. 26 83 (2004)
  24. Bingi V N, Savin A V Uspekhi Fizicheskikh Nauk 173 265 (2003)
  25. Martin A P Progress In Oceanography 57 125 (2003)

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