Issues

 / 

2002

 / 

January

  

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
URL: https://ufn.ru/en/articles/2002/1/b/
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)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

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. Haken H Synergetics. An Introduction (Springer Series in Synergetics, Vol. 1, Berlin: Springer-Verlag, 1977)
  2. Nicolis G, Prigogine I Self-organization in Nonequilibrium Systems (New York: Wiley, 1977)
  3. Weidlich W, Haag G Concepts and Models of a Quantitative Sociology. The Dynamics of Interacting Populations (Springer Series in Synergetics, Vol. 14, Berlin: Springer-Verlag, 1983)
  4. Turing A M Philos. Trans. R. Soc. London Ser. B 237 37 (1952)
  5. Medvinsky A B et al., in Self-organization of Complex Structures. From Individual to Collective Dynamics (Ed. F Schweitzer, Amsterdam: Gordon and Breach Sci. Publ., 1997) p. 269
  6. De Kepper P et al. Physica D 49 161 (1991)
  7. Shemyakin F M, Mikhalev P F Fiziko-Khimicheskie Periodicheskie Protsessy (Physico-Chemical Periodic Processes, Moscow-Leningrad: Izd. AN SSSR, 1938)
  8. Romanovskiî Yu M, Stepanova N V, Chernavskiî D S Matematicheskaya Biofizika (Mathematical Biophysics, Moscow: Nauka, 1984)
  9. Sommer U Planktologie (Berlin: Springer, 1994)
  10. Sommer U Algen, Quallen, Wasserfloh. Die Welt des Planktons (Berlin: Springer, 1996)
  11. Baretta-Bekker J G, Duursma E K, Kuipers B R (Eds) Encyclopedia of Marine Sciences 2nd ed. (New York: Springer, 1998)
  12. Raymont J E G Plankton and Productivity in the Oceans (Oxford: Pergamon Press, 1980-1983)
  13. Hallegraeff G M Plankton. A Microscopic World (Leiden: E.J. Brill, 1988)
  14. Hensen V Ergebnisse in dem Atlantischen Ocean von Mitte Juli bis Anfang November 1889 ausgeführten Plankton-Expedition der Humboldt-Stiftung (Leipzig: Kiel, 1892)
  15. Porep R, in Kieler Beiträge zür Geschichte der Medizin und Pharmazic Vol. 9 (Eds R Herrlinger, F Kudlien, G E Dann, Neumünster: Karl Wachholtz, 1970)
  16. Bain R C (Jr.) J. Sanitary Engineering Division (October) 867 (1968)
  17. Ritschard R L Water Air Soil Poll. 64 289 (1992)
  18. Malin G Nature 387 857 (1997)
  19. Charlson R J et al. Nature 326 655 (1987)
  20. Williamson P, Gribbin J New Sci. (16 March) 48 (1991)
  21. Lotka A J Elements of Physical Biology (Baltimore: Williams & Wilkins Co., 1925)
  22. Volterra V J. Cons. Perm. Int. l’Explor. Mer. 3 3 (1926)
  23. Cushing D H Marine Ecology and Fisheries (Cambridge: Cambridge Univ. Press, 1975)
  24. Gulland J A (Ed.) Fish Population Dynamics (London: Wiley, 1977)
  25. Steele J H (Ed.) Fisheries Mathematics: The Proc. of a Conf., Aberdeen, 1975 (London: Academic Press, 1977)
  26. Fleming R H J. Cons. Perm. Int. l’Explor. Mer. 14 210 (1939)
  27. Ivlev V S Usp. Sovremennoî Biol. XIX 98 (1945)
  28. Riley G A J. Mar. Res. 6 54 (1946)
  29. Odum H T Limnol. Oceanogr. 1 102 (1956)
  30. Droop M R Bot. Mar. XXVI 99 (1983)
  31. Behrenfeld M J, Falkowski P G Limnol. Oceanogr. 42 1479 (1997)
  32. Riley G A, in The Sea Vol. 2 (Ed. M N Hill, London: Wiley, 1963) p. 436
  33. Segel L A, Jackson J L J. Theor. Biol. 37 545 (1972)
  34. Dubois D Ecol. Model. 1 67 (1975)
  35. Levin S A, Segel L A Nature 259 659 (1976)
  36. Mimura M, Murray J D J. Theor. Biol. 75 249 (1978)
  37. Mayzaud P, Poulet S A Limnol. Oceanogr. 23 1144 (1978)
  38. Holling C S Can. Entomol. 91 385 (1959)
  39. Michaelis L, Menten M Biochem. Z. 49 333 (1913)
  40. Monod J, Jacob F Cold Spring Harb. Symp. 26 389 (1961)
  41. Steele J H, Henderson E W Am. Nat. 117 676 (1981)
  42. Steele J H, Henderson E W J. Plankton Res. 14 157 (1992)
  43. Steele J H, Henderson E W J. Plankton Res. 14 1397 (1992)
  44. Scheffer M OIKOS 62 271 (1991)
  45. Scheffer M Ecology of Shallow Lakes (Population and Community Biology Series, Vol. 22, London: Chapman & Hall, 1997)
  46. Malchow H Proc. R. Soc. London Ser. B 251 103 (1993)
  47. Truscott J E, Brindley J Bull. Math. Biol. 56 981 (1994)
  48. Truscott J E, Brindley J Philos. Trans. R. Soc. London Ser. A 347 703 (1994)
  49. Beltrami E Estuaries 12 13 (1989)
  50. Beltrami E Environ. Model. Assess. 1 19 (1996)
  51. DeЂAngelis D L Dynamics of Nutrient Cycling and Food Webs (Population and Community Biology Series, Vol. 9, London: Chapman & Hall, 1992)
  52. Jörgensen S E Fundamentals of Ecological Modelling 2nd ed. (Amsterdam: Elsevier, 1994)
  53. Yodzis P, in Frontiers in Mathematical Biology (Lecture Notes in Biomathematics, Vol. 100, Ed. S A Levin, Berlin: Springer-Verlag, 1994)
  54. May R Science 186 645 (1974)
  55. Scheffer M J. Plankton Res. 13 1291 (1991)
  56. Godfray C, Hassell M Science 275 323 (1997)
  57. Huisman J, Weissing F J Nature 402 407 (1999)
  58. Pascual M Proc. R. Soc. London Ser. B 251 1 (1993)
  59. Petrovskii S V, Malchow H Math. Comput. Model. 29 49 (1999)
  60. Petrovskii S V, Malchow H Theor. Popul. Biol. 59 157 (2001)
  61. Evans G T, Parslow S Biol. Oceanogr. 3 327 (1985)
  62. Truscott J E J. Plankton Res. 17 2207 (1995)
  63. Popova E E et al. J. Plankton Res. 19 1495 (1997)
  64. Ascioti F A et al. J. Plankton Res. 15 603 (1993)
  65. Kuznetsov Yu A, Muratori S, Rinaldi S Int. J. Bifurcat. Chaos 2 117 (1992)
  66. Rinaldi S, Muratori S Ecol. Model. 69 79 (1993)
  67. Steffen E, Malchow H, in Self-organization of Complex Structures. From Individual to Collective Dynamics (Ed. F Schweitzer, Amsterdam: Gordon and Breach Sci. Publ., 1997) p. 331
  68. Steffen E, Malchow H Senckenbergiana Maritima 27 137 (1996)
  69. Steffen E, Malchow H, Medvinsky A B Environ. Model. Assess. 2 43 (1997)
  70. Scheffer M et al. OIKOS 80 519 (1997)
  71. Fasham M J R Oceanogr. Mar. Biol. Ann. Rev. 16 43 (1978)
  72. Steele J H (Ed.) Spatial Pattern in Plankton Communities (NATO Conf. Ser. IV, Marine Sciences, Vol. 3, New York: Plenum Press, 1978)
  73. Mackas D L, Boyd C M Science 204 62 (1979)
  74. Greene C H et al. Limnol. Oceanogr. 37 650 (1992)
  75. Abbott M, in Patch Dynamics (Lecture Notes in Biomathematics, Vol. 96, Eds S A Levin, T M Powell, J H Steele, Berlin: Springer-Verlag, 1993) p. 37
  76. Novikov I Ya, Stechkin S B Usp. Mat. Nauk 53 (6) 53 (1998) [Russ. Math. Surv. 53 1159 (1998)]
  77. Dremin I M, Ivanov O V, Nechitaîlo V A Usp. Fiz. Nauk 171 465 (2001) [Phys. Usp. 44 447 (2001)]
  78. Platt T Deep-Sea Res. 19 183 (1972)
  79. Denmann K L Deep-Sea Res. 23 539 (1976)
  80. Stommel H J. Mar. Res. 8 24 (1948)
  81. Leibovich S, in Patch Dynamics (Lecture Notes in Biomathematics, Vol. 96, Eds S A Levin, T M Powell, J H Steele, Berlin: Springer-Verlag, 1993) p. 110
  82. Yoder J A et al. Nature 371 689 (1994)
  83. Franks P J S Limnol. Oceanogr. 42 1297 (1997)
  84. Abraham E R Nature 391 577 (1998)
  85. Platt J R Science 133 1766 (1961)
  86. Winet H, Jahn T Biorheology 9 87 (1972)
  87. Pedley T J, Kessler J O Ann. Rev. Fluid Mech. 24 313 (1992)
  88. Timm U, Okubo A Bull. Math. Biol. 56 187 (1994)
  89. Witten T A (Jr.), Sander L M Phys. Rev. Lett. 47 1400 (1981)
  90. Matsushita M, Fujikawa H Physica A 168 498 (1990)
  91. Ben-Jacob E et al. Physica A 87 378 (1992)
  92. Okubo A Diffusion and Ecological Problems. Mathematical Models (Biomathematics, Vol. 10, Berlin: Springer-Verlag, 1980)
  93. Holmes E E et al. Ecology 75 17 (1994)
  94. Malchow H Ecol. Model. 75/76 123 (1994)
  95. Kierstead H, Slobodkin L B J. Mar. Res. XII 141 (1953)
  96. Skellam J G Biometrika 38 196 (1951)
  97. Luther R Z. Electrochemie 12 596 (1906)
  98. Fisher R A Ann. Eugenics 7 355 (1937)
  99. Kolmogorov A, Petrovskii I, Piskunov N Bull. Univ. Moscow, Ser. Intern. Sect. A 1 1 (1937)
  100. Allee W C Animal Aggregations: A Study in General Sociology (Chicago: The Univ. of Chicago Press, 1931)
  101. Allee W C et al. Principles of Animal Ecology (Philadelphia: Saunders Co., 1949)
  102. Schlögl F Z. Phys. 253 147 (1972)
  103. Nitzan A, Ortoleva P, Ross J Faraday Symp. Chem. Soc. 9 241 (1974)
  104. Ebeling W, Schimansky-Geier L, in Proc. 6th Intern. Conf. on Thermodynamics (Merseburg, 1980) p. 95
  105. Malchow H, Schimansky-Geier L Noise and Diffusion in Bistable Nonequilibrium Systems (Teubner-Texte zur Physik, Bd. 5, Leipzig: Teubner, 1985)
  106. Lewis M A, Kareiva P Theor. Popul. Biol. 43 141 (1993)
  107. Petrovskiî S V Inzh. Fiz. Zh. 66 398 (1994) [J. Eng. Phys. Thermophys. 66 346 (1994)]
  108. Ludwig D, Jones D D, Holling C S J. Anim. Ecol. 47 315 (1978)
  109. Wissel C Theoretische Ökologie (Berlin: Springer, 1989)
  110. Field R J, Burger M (Eds) Oscillations and Traveling Waves in Chemical Systems (New York: Wiley, 1985)
  111. Wyatt T Mar. Biol. 22 137 (1973)
  112. Boerlijst M C, Lamers M E, Hogeweg P Proc. R. Soc. London Ser. B 253 15 (1993)
  113. Adler J Science 153 708 (1966)
  114. Adler J, Templeton B J. Gen. Microbiol. 46 (Pt. 2) 175 (1967)
  115. Gerisch G, in Current Topics in Developmental Biology Vol. 3 (Eds A A Moscona, A Monroy, New York: Academic, 1968) p. 157
  116. Gerisch G Naturwissenschaften 58 430 (1971)
  117. Keller E F, Segel L A J. Theor. Biol. 26 399 (1970)
  118. Keller E F, Segel L A J. Theor. Biol. 30 225 (1971)
  119. Keller E F, Segel L A J. Theor. Biol. 30 235 (1971)
  120. Segel L A, Stoeckly B J. Theor. Biol. 37 561 (1972)
  121. Segel L A SIAM J. Appl. Math. 32 653 (1977)
  122. Newell P C, in Fungal Differentiation. A Contemporary Synthesis (Mycology Series, Vol. 4, Ed. J E Smith, New York: M. Dekker, 1983) p. 43
  123. Alt W, Hoffmann G (Eds) Biological Motion (Lecture Notes in Biomathematics, Vol. 89, Berlin: Springer-Verlag, 1990)
  124. Ivanitskiî G R, Medvinskiî A B, Tsyganov M A Usp. Fiz. Nauk 161 (4) 13 (1991) [Sov. Phys. Usp. 34 289 (1991)]
  125. Ivanitskiî G R, Medvinskiî A B, Tsyganov M A Usp. Fiz. Nauk 164 1041 (1994) [Phys. Usp. 37 961 (1994)]
  126. Medvinsky A B et al. FEMS Microbiol. Lett. 84 279 (1991)
  127. Medvinsky A B et al. FEMS Microbiol. Lett. 112 287 (1993)
  128. Medvinsky A B et al. Physica D 64 267 (1993)
  129. Medvinsky A B et al. Physica D 79 299 (1994)
  130. Medvinskiî A B et al. Dokl. Ross. Akad. Nauk 338 690 (1994)
  131. Siegert F, Weijer C J Physica D 49 224 (1991)
  132. Steinbock G, Hashimoto H, Müller S C Physica D 49 233 (1991)
  133. Reshetilov A N et al. FEMS Microbiol. Lett. 94 59 (1992)
  134. Vasiev B N, Hogeweg P, Panfilov A V Phys. Rev. Lett. 73 3173 (1994)
  135. Höfer T, Sherratt J A, Maini P K Physica D 85 425 (1995)
  136. Sherratt J A, Lewis M A, Fowler A C Proc. Natl. Acad. Sci. USA 92 2524 (1995)
  137. Sherratt J A, Eagan B T, Lewis M A Philos. Trans. R. Soc. London Ser. B 352 21 (1997)
  138. Merkin J H et al. Phys. Rev. Lett. 76 546 (1996)
  139. Davidson F A Int. J. Bifurcat. Chaos 8 1303 (1998)
  140. Rovinsky A B, Menzinger M Phys. Rev. Lett. 69 1193 (1992)
  141. Malchow H J. Marine Syst. 7 193 (1996)
  142. Malchow H Z. Phys. Chem. 204 35 (1998)
  143. Daly K L, Smith W O (Jr.) Ann. Rev. Ecol. Syst. 24 555 (1993)
  144. O’Brien J J, Wroblewski J S J. Theor. Biol. 38 197 (1973)
  145. Wroblewski J S, O’Brien J J, Platt T Mémoires Soc. R. Sci. Liège VII 43 (1975)
  146. Wroblewski J S, O’Brien J J Mar. Biol. 35 161 (1976)
  147. Malchow H, Shigesada N Nonlinear Proc. Geophys. 1 3 (1994)
  148. Wyatt T Thalassia Jugoslavica 7 435 (1971)
  149. Nakata K, Ishikawa R Jpn. J. Ecol. 25 201 (1975)
  150. Powell T M et al. Science 189 1088 (1975)
  151. Weber L H, El-Sayed S Z, Hampton I Deep-Sea Res. 33 1327 (1986)
  152. Murray J D Mathematical Biology (Berlin: Springer-Verlag, 1989)
  153. Levin S A, Powell T M, Steele J H (Eds) Patch Dynamics (Lecture Notes in Biomathematics, Vol. 96, Berlin: Springer-Verlag, 1993)
  154. Dunbar S R SIAM J. Appl. Math. 46 1057 (1986)
  155. Petrovsky S V, Vinogradov M E, Morozov A Yu Okeanologiya 38 881 (1998) [Oceanology 38 796 (1998)]
  156. Petrovskii S V, Malchow H Nonlinear Anal.: Real World Appl. 1 37 (2000)
  157. Kopell N, Howard L N Stud. Appl. Math. 52 291 (1973)
  158. Nayfeh A H, Balachandran B Applied Nonlinear Dynamics (New York: Wiley, 1995)
  159. Fedorov K N, Ginzburg A I Pripoverkhnostnyî Sloî Okeana (The Subsurface Layer in the Ocean, Leningrad: Gidrometeoizdat, 1988)
  160. Ozmidov R V Gorizontal’naya Turbulentnost’ i Turbulentnyî Obmen v Okeane (Horizontal Turbulence and Turbulent Exchange in the Ocean, Moscow: Nauka, 1968)
  161. Okubo A Deep-Sea Res. 18 789 (1971)
  162. Petrovskii S V J. Marine Syst. 21 179 (1999)
  163. Ozmidov R V Okeanologiya 38 7 (1998) [Oceanology 38 3 (1998)]
  164. Holland J H Adaptation in Natural and Artificial Systems (Ann Arbor: Univ. of Michigan Press, 1975)
  165. Scheffer M et al. Ecol. Model. 80 161 (1995)
  166. Savill N J, Hogeweg P J. Theor. Biol. 184 229 (1997)
  167. Radakov D V Staînost’ Ryb Kak Ekologicheskoe Yavlenie (Schooling in the Ecology of Fish, Moscow: Nauka, 1972) [Translated into English (New York: J. Wiley, 1973)]
  168. Blake R W Fish Locomotion (Cambridge: Cambridge Univ. Press, 1983)
  169. Okubo A Adv. Biophys. 22 1 (1986)
  170. Semovskiî S V Mat. Modelirovanie 1 (6) 49 (1989)
  171. Grünbaum D, Okubo A, in Frontiers in Mathematical Biology (Lecture Notes in Biomathematics, Vol. 100, Ed. S A Levin, Berlin: Springer-Verlag, 1994) p. 296
  172. Huth A, Wissel C Ecol. Model. 75/76 135 (1994)
  173. Reuter H, Breckling B Ecol. Model. 75/76 147 (1994)
  174. Gueron S, Levin S A, Rubenstein D I J. Theor. Biol. 182 85 (1996)
  175. Niwa H-S J. Theor. Biol. 181 47 (1996)
  176. Romey W L Ecol. Model. 92 65 (1996)
  177. Flierl G et al. J. Theor. Biol. 196 397 (1999)
  178. Stöcker S Math. Biosci. 156 167 (1999)
  179. Goodwin R M, in Socialism, Capitalism and Economic Growth (Ed. C H Feinstein, London: Cambridge Univ. Press, 1967) p. 54
  180. Lorenz H-W Nonlinear Dynamical Economics and Chaotic Motion 2nd ed. (Berlin: Springer-Verlag, 1993)
  181. Ruth M, Hannon B Modeling Dynamic Economic Systems (New York: Springer, 1997)
  182. Malchow H et al. Nonlinear Anal.: Real World Appl. 1 53 (2000)
  183. Medvinsky A B et al. Nonlinear Dynam. Psychol. Life Sci. 4 135 (2000)
  184. Tikhonov D A et al. Chaos Soliton. Fract. 12 277 (2000)
  185. Tikhonova I A et al. Biofiz. 45 352 (2000) [Biophys. 45 343 (2000)]
  186. Bocharov L N Sistemnyî Analiz v Kratkosrochnom Rybopromyslovom Prognozirovanii (Systemic Analysis in Short-Term Fishery Forecasts, Leningrad: Nauka, 1990)
  187. Ebenhöh W Model. Ident. Control 1 69 (1980)
  188. Fernö A et al. Sarsia 83 149 (1998)
  189. Misund O A et al. Sarsia 83 117 (1998)
  190. Murray J D Lectures on Nonlinear-Differential-Equation Models in Biology (Oxford: Clarendon, 1977)
  191. Winfree A T The Geometry of Biological Time (Biomathematics, Vol. 8, New York: Springer-Verlag, 1980)
  192. Winfree A T When Time Breaks Down (Princeton, N.J.: Princeton Univ. Press, 1987)
  193. Krinskiî V I, Medvinskiî A B, Panfilov A V Evolyutsiya Avtovolnovykh Vikhreî. Volny v Serdtse (Evolution of Autowave Vortices. Waves in the Heart, Moscow: Znanie, 1986)
  194. Grusa K-U Mathematical Analysis of Nonlinear Dynamic Processes (Harlow: Longman Scientific & Technical, 1988)
  195. Biktashev V N et al. Phys. Rev. Lett. 81 2815 (1998)
  196. Mandelbrot B B Fractals: Form, Chance, and Dimension (San Francisco: W.H. Freeman, 1977)
  197. Mandelbrot B B The Fractal Geometry of Nature (San Francisco: W.H. Freeman, 1982)
  198. Feder J Fractals (New York: Plenum Press, 1988)
  199. Schroeder M R Fractals, Chaos, Power Laws (New York: W.H. Freeman, 1991)
  200. Peitgen H-O, Jürgens H, Saupe D Chaos and Fractals: New Frontiers of Science (New York: Springer-Verlag, 1992)
  201. Bacry E, Muzy J F, Arneodo A J. Stat. Phys. 70 635 (1993)
  202. Arneodo A et al. Physica D 96 291 (1996)
  203. Muzy J F, Bacry E, Arneodo A Phys. Rev. E 47 875 (1993)
  204. Arneodo A, Bacry E, Muzy J F Physica A 213 232 (1995)
  205. Meyer Y Ondelettes et Opérateurs (Paris: Hermann, 1989) [Translated into English: Wavelets and Operators (Cambridge: Cambridge Univ. Press, 1992)]
  206. David G Wavelets and Singular Integrals on Curves and Surfaces (Berlin: Springer-Verlag, 1991)
  207. Kahane J P, Lemarié-Rieusset P G Fourier Series and Wavelets (London: Gordon & Breach, 1995)
  208. Hubbard B B The World According to Wavelets. The Story of a Mathematical Technique in the Making (Wellesley, Mass.: A K Peters, 1996)
  209. Chhabra A B et al. Phys. Rev. A 40 5284 (1989)
  210. Phillips O M The Dynamics of the Upper Ocean 2nd ed. (Cambridge: Cambridge Univ. Press, 1977)
  211. Pond S, Pickard G L Introductory Dynamic Oceanography (Oxford: Pergamon Press, 1978)
  212. Pedlosky J Geophysical Fluid Dynamics 2nd ed. (New York: Springer-Verlag, 1987)
  213. Pedlosky J Ocean Circulation Theory (Berlin: Springer, 1996)
  214. Vozjinskaya V B Oceanology 4 876 (1964)
  215. Abbot M R, Zion P M Cont. Shelf Res. 4 661 (1985)
  216. Walsh J J et al. Prog. Oceanogr. 23 245 (1989)
  217. Capella J E et al. Deep-Sea Res. 39 1201 (1992)
  218. Sur H I et al. J. Marine Syst. 7 293 (1996)
  219. MacKenzie B R et al. Limnol. Oceanogr. 39 1790 (1994)
  220. Jenkinson I R, Biddanda B A J. Plankt. Res. 17 2251 (1995)
  221. Marrase C, Saiz E, Redondo J M (Eds) Lectures on Plankton and Turbulence (Scientia Marina, Vol. 61, Suppl. 1, Barcelona: Intern. Centre for Coastal Resources Res., 1997)
  222. Nihoul J C J (Ed.) Marine Turbulence (Elsevier Oceanography Series, Vol. 28, Amsterdam: Elsevier, 1980)
  223. Monin A S, Ozmidov R V Okeanskaya Turbulentnost’ (Ocean Turbulence, Leningrad: Gidrometeoizdat, 1981) [Translated into English: Turbulence in the Ocean (Dordrecht: Reidel, 1985)]
  224. Barenblatt G I, Galerkina N L, Luneva M V Inzh. Fiz. Zh. 53 733 (1987) [J. Eng. Phys. Thermophys. 53 733 (1987)]
  225. Barenblatt G I Scaling, Self-similarity, and Intermediate Asymptotics (Cambridge: Cambridge Univ. Press, 1996)
  226. Ozmidov R V Okeanologiya 6 393 (1966)
  227. Laurs R M, Fidler P C, Montgomery D R Deep-Sea Res. 31 1085 (1984)
  228. Hofmann E E et al. Deep-Sea Res. 39 1177 (1992)
  229. Hood R R et al. J. Geophys. Res. 95 18081 (1990)
  230. Barnard A H, Stegmann P M, Yoder J A Cont. Shelf Res. 17 1181 (1997)
  231. Njoku E G et al. J. Geophys. Res. 90 11573 (1985)
  232. Rodionov V B, Kostyanoî A G Okeanicheskie Fronty Moreî Severo-Evropeîskogo Basseîna (Ocean Fronts in the North-European Basin, Moscow: GEOS, 1998)
  233. Monin A S, Kamenkovich V M, Kort V G Izmenchivost’ Mirovogo Okeana (Variability of the World’s Ocean, Leningrad: Gidrometeoizdat, 1974) [Translated into English: Variability of the Ocean (New York: Wiley, 1977)]
  234. Monin A S, Krasitskiî V P Yavleniya na Poverkhnosti Okeana (Surface Phenomena in the Ocean, Leningrad: Gidrometeoizdat, 1985)
  235. Foster T D, in Processus de Formation des Eaux Oceaniques Profondes, en Particulier en Mediterranee Occidentale, Paris, 1972 (Colloques Intern. Du Centre National de la Recherche Scientifique, N 215, Paris: CNRS, 1974) p. 237
  236. Joseph D D Stability of Fluid Motions (Springer Tracts in Natural Philosophy, Vol. 27-28, Berlin: Springer-Verlag, 1976)
  237. Fedorov K N Fizicheskaya Priroda i Struktura Okeanicheskikh Frontov (Nature and Structure of Ocean Fronts, Leningrad: Gidrometeoizdat, 1983) [Translated into English: The Physical Nature and Structure of Oceanic Fronts (Berlin: Springer-Verlag, 1986)]
  238. Fiedler P C, Bernard H J Cont. Shelf Res. 7 871 (1987)
  239. Mackas D L, Washburn L, Smith S L J. Geophys. Res. 96 14781 (1991)
  240. Kamenkovich V M, Koshlyakov M N, Monin A S Sinopticheskie Vikhri v Okeane 2nd ed. (Synoptic Eddies in the Ocean, Leningrad: Gidrometeoizdat, 1987) [Translated into English (Dordrecht: D. Reidel, 1986)]
  241. Sverdrup H U J. Mar. Res. 1 115 (1938)
  242. The Ring Group Science 212 1091 (1981)
  243. The Coastal Transition Zone Group EOS 69 669 (1988)
  244. Barth J A J. Geophys. Res. 94 10844 (1989)
  245. Angel M V, Fasham M J R, in Eddies in Marine Science (Ed. A R Robinson, Berlin: Springer-Verlag, 1983) p. 492
  246. Haury L R et al. J. Geophys. Res. 91 12937 (1986)
  247. Hayward T L, Mantyla A W J. Mar. Res. 48 825 (1990)
  248. Bucklin A J. Geophys. Res. 96 14799 (1991)
  249. Bowman M J et al., in Coastal Oceanography (NATO Conf. Series, Ser. IV: Marine Sciences, Vol. 11, Eds H G Gade, A Edwards, H Svendsen, New York: Plenum Press, 1983) p. 279
  250. Wiebe P H et al. Deep-Sea Res. 23 695 (1976)
  251. Armi L, Zenk W J. Phys. Oceanogr. 14 1560 (1984)
  252. Armi L et al. Nature 333 649 (1988)
  253. Kostianoy A G, Belkin I M, in Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence (Elsevier Oceanography Series, Vol. 50, Eds J C J Nihoul, B M Jamart, Amsterdam: Elsevier, 1989) p. 821
  254. Cooper L H N, in Oceanography: Invited Lectures Presented at the Intern. Oceanographic Congress, New York, 1959 (Publ. AAAS, Vol. 67, Ed. M Sears, Washington: AAAS, 1961) p. 599
  255. Nisbet R M et al., in Patch Dynamics (Lecture Notes in Biomathematics, Vol. 96, Eds S A Levin, T M Powell, J H Steele, Berlin: Springer-Verlag, 1993)
  256. Ranta E, Kaitala V, Lundberg P Science 278 1621 (1997)
  257. Scheffer M Hydrobiol. Bull. 23 73 (1989)
  258. Wilson D S Ecology 73 1984 (1992)
  259. Allen J C, Scheffer W M, Rosko D Nature 364 229 (1993)
  260. Hastings A Ecology 74 1362 (1993)
  261. Pahl-Wostl C Theor. Popul. Biol. 43 159 (1993)
  262. Garfinkel A et al. Science 257 1230 (1992)
  263. West B J, Deering B The Lure of Modern Science: Fractal Thinking (Studies of Nonlinear Phenomena in Life Sciences, Vol. 3, Singapore: World Scientific, 1995)
  264. Marks-Tarlow T Nonlinear Dynam. Psychol. Life Sci. 3 311 (1999)
  265. Lipsitz L, Goldberger A J. Am. Med. Assoc. 267 1806 (1992)
  266. Medvinsky A B et al. J. Bioscience 26 77 (2001)
  267. Medvinsky A B et al. J. Bioscience 26 109 (2001)
  268. Astaf’eva N M Usp. Fiz. Nauk 166 1145 (1996) [Phys. Usp. 39 1085 (1996)]

© 1918–2019 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions