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Reviews of topical problems


Self-organization in active distributed media: scenarios for the spontaneous formation and evolution of dissipative structures

,  a
a Institute of Electrophysics, Ural Branch of the Russian Academy of Sciences, ul. Amundsena 106, Ekaterinburg, 620016, Russian Federation

Various scenarios for self-organization in a wide range of nonequilibrium physical, chemical, and biological systems are examined. It is stressed that in many systems small-amplitude dissipative structures never form: At the instant at which the homogeneous state stratifies, large-amplitude dissipative structures appear abruptly. These large-amplitude structures are striations, spots, or blobs. Methods for the construction of such dissipative structures and for studying their stability are discussed for an arbitrary departure of the system from equilibrium. Many self-organization scenarios do not involve an instability of the dissipative structures of a given type and are instead determined by a local breakdown effect. In real systems, self-organization is determined by the spontaneous appearance and subsequent evolution of autosolitons (localized dissipative structures). The conditions under which turbulence arises in such systems in the absence of a flow are discussed. This turbulence is a complicated picture of the random appearance and disappearance of interacting autosolitons in various parts of the system. In gaseous and semiconductor plasmas, dissipative structures can arise in the form of numerous current filaments or electric-field domains. Their formation is unrelated to the shape of the current-voltage characteristic of the system. There is a discussion of certain self-organization phenomena in systems in which static dissipative structures may be accompanied by pulsating dissipative structures and autowaves. Corresponding effects in systems with flows (or fluxes of material) are also discussed. The general results of self-organization theory are used to explain the properties of the dissipative structures which have been observed and studied in numerical and experimental studies of physical systems of various types in recent years.

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Fulltext is also available at DOI: 10.1070/PU1990v033n09ABEH002627
PACS: 47.27.−i, 72.30.+q (all)
DOI: 10.1070/PU1990v033n09ABEH002627
URL: https://ufn.ru/en/articles/1990/9/a/
Citation: Kerner B S, Osipov V V "Self-organization in active distributed media: scenarios for the spontaneous formation and evolution of dissipative structures" Sov. Phys. Usp. 33 (9) 679–719 (1990)
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Оригинал: Кернер Б С, Осипов В В «Самоорганизация в активных распределенных средах (Сценарии спонтанного образования и эволюции диссипативных структур)» УФН 160 (9) 1–73 (1990); DOI: 10.3367/UFNr.0160.199009a.0001

References (179) ↓ Cited by (103) Similar articles (20)

  1. Landau L. D., Lifshits E. M. Gidrodinamika (M.: Nauka, 1986)
  2. a, Dzhozef D. Ustoichivost’ Dvizhenii Zhidkosti (M: Mir, 1981); b, Gershuni G, Z., Zhukhovitskii E. M., Nepomnyashchii A. A. Ustoichivost’ Konvektivnykh Techenii (M.: Nauka, 1989)
  3. Nikolis G., Prigozhin I. Samoorganizatsiya v Neravnovesnykh Sistemakh (M.: Mir, 1979)
  4. Ebeling V. Obrazovanie Struktur pri Neobratimykh Protsessakh (M.: Mir, 1979)
  5. Khaken G. Sinergetika (M.: Mir, 1980)
  6. Khaken G. Sinergetika: Ierarkhii Neustoichivostei v Samoorganizuyushchikhsya Sistemakh i Ustroistvakh (M.: Mir, 1985)
  7. a, Wiener N., Rosenblueth A. Arch. Inct. Cardiol. Mech. 16 205 (1946); b, Polak L. S., Mikhailov A. S. Samoorganizatsiya v Neravnovesnykh Fiziko-khimicheskikh Sistemakh (M.: Nauka, 1983)
  8. a, Vasil’ev V. A., Romanovskii Yu. M., Yakhno V. G. Usp. Fiz. Nauk 128 625 (1979); Vasil’ev V A, Romanovskii Yu M, Yakhno V G Sov. Phys. Usp. 22 615 (1979); b, Vasil’ev V. A., Romanovskii Yu. M., Yakhno V. G. Avtovolnovye Protsessy (M.: Nauka, 1987)
  9. Gaponov-Grekhov A. V., Rabinovich M. I. Nelineinye Volny: Struktury i Bifurkatsii (M.: Nauka, 1987) p. 7
  10. Zhabotinskii A. M. Kontsentratsionnye Kolebaniya (M.: Nauka, 1974)
  11. a, Romanovskii Yu. M., Stepanova N. V., Chernavskii D. S. Matematicheskoe Modelirovanie v Biofizike (M.: Nauka, 1975); b, Romanovskii Yu. M., Stepanova N. V., Chernavskii D. S. Matematicheskaya Biofizika (M.: Nauka, 1984)
  12. Belintsev B. N. Usp. Fiz. Nauk 141 55 (1983); Belintsev B N Sov. Phys. Usp. 26 775 (1983)
  13. Sivashinsky G I Annu. Rev. Fluid Mech. 15 179 (1983)
  14. a, Nedospasov A. V. Usp. Fiz. Nauk 94 439 (1968); Nedospasov A V Sov. Phys. Usp. 11 174 (1968); Nedospasov A. V., Khait V. D. Kolebaniya i Neustoichivosti Nizkotemperaturnoi Plazmy (M.: Nauka, 1979); b, Pekarek L. Usp. Fiz. Nauk 94 463 (1968); Pekarek L Sov. Phys. Usp. 11 188 (1968)
  15. Kadomtsev B. B. Nelineinye Volny: Struktury i Bifurkatsii (M.: Nauka, 1987) p. 45
  16. Kolebaniya i Begushchie Volny v Khimicheskikh Sistemakh (M.: Mir, 1988)
  17. Vasilev V. A., Romanovskii Yu. M., Chernavskii D. S., Yakhno V. G. Autowave Processes In Kinetic Systems (Berlin: Veb Deutscher Verlag der Wissenschaften; Dordrecht: D. Reidel, 1987)
  18. Landa P. S. Avtokolebaniya v Raspredelennykh Sistemakh (M.: Nauka, 1983)
  19. Gurevich A. V., Mints R. G. Teplovye Avtovolny v Normal’nykh Metallakh i Sverkhprovodnikakh (M.: IVT AN SSSR, 1987)
  20. Merzhanov A. G., Rumanov E. N. Usp. Fiz. Nauk 151 553 (1987); Merzhanovand A G, Rumanov E N Sov. Phys. Usp. 30 293 (1987)
  21. Volkov A. V., Kogan. Sh. M. Usp. Fiz. Nauk 96 633 (1968); Volkov A V, Kogan Sh M Sov. Phys. Usp. 11 881 (1968)
  22. Osipov V. V., Kholodnoe V. A. Mikroelektronika 2 529 (1973)
  23. Bonch-Bruevich V. L., Zvyagin I. P., Mironov A. G. Domennaya Elektricheskaya Neustoichivost’ v Poluprovodnikakh (M.: Nauka, 1972)
  24. Scholl E Nonequilibrium Phase Transitions In Semiconductors (Springer Series in Synergetics) Vol. 35 (Berlin: Springer-Verlag, 1987)
  25. Kerner B. S., Osipov V. V. Usp. Fiz. Nauk 157 201 (1989); Kerner B S, Osipov V V Sov. Phys. Usp. 32 101 (1989)
  26. Andronov A. A., Vitt A. A., Khaikin S. E. Teoriya Kolebanii (M.: Fizmatgiz, 1959)
  27. Gaponov-Grekhov A, V., Rabinovich M. I. Usp. Fiz. Nauk 128 579 (1979); Gaponov-Grekhov A V, Rabinovich M I Sov. Phys. Usp. 22 590 (1979)
  28. Rabinovich M. I., Trubetskov D. M. Vvedenie v Teoriyu Kolebanii i Voln (M.: Nauka, 1984)
  29. Zaslavskii G. I., Sagdeev R. 3. Vvedenie v Nelineinuyu Fiziku (M: Nauka, 1988)
  30. Klimontovich Yu. L. Usp. Fiz. Nauk 158 59 (1989); Klimontovich Yu L Sov. Phys. Usp. 32 416 (1989)
  31. a, Kerner B. S., Sinkevich V. F. Pis’ma ZhETF 36 359 (1982); Kerner B S, Sinkevich V F JETPLett. 36 436 (1982); b, Kerner B. S., Osipov V. V., Romanko M. T., Sinkevich V. F. Pis’ma ZhETF 44 77 (1986); Kerner B S et al. JETP Lett. 44 97 (1986); Vashchenko V. A., Kerner B. S., Osipov V. V., Sinkevich V. F. Fiz. Tekh. Poluprovodn. 23 1378 (1989); Bashchenko V A et al. Sov. Phys. Semicond. 23 857 (1989)
  32. Mauer K. M., Parisi J., Huebener R. P. Z. Phys. B 71 171 (1988)
  33. a, Jäger D, Baumann H., Symancyk R. Phys. Lett. A 117 141 (1986); b, Gorbatyuk A. V., Liniichuk I. A., Svirin A. V. Pis’ma ZhTF 15 42 (1989); Gorbatyuk A V, Liniichuk I A, Svirin A V Sov. Tech. Phys. Lett. 15 224 (1989)
  34. Kerner B. S., Litvin D. P., Sankin V. I. Pis’ma ZhTF 13 819 (1987); Kerner B S, Litvin D P, Sankin V I Sov. Tech. Phys. Lett. 13 342 (1987)
  35. Vashchenko V. A., Kerner B. S., Osipov V. V., Sinkevich V. F. Fiz. Tekh. Poluprovodn. 24 (10) (1990)
  36. Radehaus S. R., Dirksmeyer T., Witlebrand H., Purwins H.OG. Phys. Lett. A 125 92 (1987)
  37. Abramov V. P., Klenov S. L. Radiotekhn. Elektron. 34 652 (1989)
  38. Akhmetov A. A., Baev V. P. Cryogenics 24 67 (1984); Keilip V. E., Kruglov S. L. Cryogenics 24 525 (1984)
  39. Langer J S Rev. Mod. Phys. 52 1 (1980); Wollkind D. J., Sriranganathan R., Oulton D. B. Physica D 12 215 (1984); McFadden G. V., Coriell S. R. Physica D 12 253 (1984)
  40. Barelko V. V., Beibutyan V. M., Volodin Yu. E., Zel’dovich Ya. B. Avtovolnovye Protsessy v Sistemakh s Diffuziei (Gor’kii: IPF AN SSSR, 1981) p. 135
  41. a, Akhmanov S. A., Vorontsov M. A. Nelineinye Volny: Dinamika i Evolyutsiya (M.: Nauka, 1989) p. 228; b, Akhmanov S. A., Vorontsov M. A., Ivanov V. Yu. Novye Fizicheskie Printsipy Opticheskoi Obrabotki Informatsii (M.: Nauka, 1989), Gl. 6
  42. Samarskii A. A., Galaktionov V. A., Kurdyumov S. P., Mikhailov A. P. Rezhimy s Obostreniem v Zadachakh dlya Kvazilineinykh Parabolicheskikh Uravnenii (M.: Nauka, 1987)
  43. Zel’dovich Ya. B. Teoriya Goreniya i Detonatsii Gazov (M.-L.: Izd-vo AN SSSR, 1944); Zel’dovich Ya. B. Izbrannye Trudy: Khimicheskaya Fizika i Gidrodinamika (M.: Nauka, 1984) p. 165
  44. Turing A M Philos. Trans. R. Soc. B 237 37 (1952)
  45. Kerner B. S., Osipov V. V. Radiotekhn. Elektron. 27 2415 (1982)
  46. a, Kerner B. S., Osipov V. V. Dokl. Akad. Nauk SSSR 257 1352 (1981); Kerner B S, Osipov V V Sov. Phys. Dokl. 26 420 (1981); b, Kerner B. S., Osipov V. V. Radiotekhn. Elektron. 28 132 (1983)
  47. Kerner B. S., Osipov V. V. Zh. Eksp. Teor. Fiz. 71 1542 (1976); Kerner B S and V V Osipov Sov. Phys. JETP 44 807 (1976)
  48. Kerner B. S., Osipov V. V. Fiz. Tekh. Poluprovodn. 13 891 (1979); Kerner B S, Osipov V V Sov. Phys. Semicond. 13 523 (1979)
  49. Kerner B. S., Osipov V. V. Fiz. Tverd. Tela 21 2342 (1979); Kerner B S, Osipov V V Sov. Phys. Solid State 21 1348 (1979)
  50. a, Gafiichuk V. V., Kerner B. S., Osipov V. V. Fiz. Tverd. Tela 23 2305 (1981); Gafilchuk V V, Kerner B S, Osipov V V Sov. Phys. Solid State 23 1348 (1981); b, Gafiichuk V. V., Kerner B. S., Osipov V. V. Fiz. Tekh. Poluprovodn. 15 2171 (1981); Gafilchuk V V, Kerner B S, Osipov V V Sov. Phys. Semicond. 15 1261 (1981); v, Gafiichuk V. V., Kerner B. S., Osipov V. V. Fiz. Tekh. Poluprovodn. 19 1871 (1985); Gafilchuk V V, Kerner B S, Osipov V V Sov. Phys. Semicond. 19 1153 (1985)
  51. Kerner B. S., Osipov V. V. Nelineinye Volny: Dinamika i Evolyutsiya (M.: Nauka, 1989) p. 127; Kerper V. S., Osipov V. V. Nonlinear Waves. I: Dynamics And Evolution (Berlin: Springer-Verlag, 1989) p. 126
  52. Kerner B. S., Osipov V. V. Pis’ma ZhETF 18 122 (1973); Kerner B S, Osipov V V JETP Lett. 18 70 (1973); Kerner B. S., Osipov V. V. Mikroelektronika 3 9 (1974)
  53. Balkarei Yu. I., Nikulin M. G. Fiz. Tekh. Poluprovodn. 10 1455 (1976); Balkarei Yu I, Nikulin M G Sov. Phys. Semicond. 10 863 (1976); Balkarei Yu. I., Nikulin M. G. Fiz. Tekh. Poluprovodn. 10 2039 (1976); Balkarei Yu I, Nikulin M G Sov. Phys. Semicond. 10 1216 (1976)
  54. Balkarei Yu. I., Elinson M. I. Mikroelektronika 8 428 (1979)
  55. Balkarei Yu. I., Evtikhov M. G., Elinson M. I. Mikroelektronika 14 67 (1985)
  56. Balkarei Yu. I., Nikulin M. G., Elinson M. I. Avtovolnovye Protsessy v Sistemakh s Diffuziei (Gor’kii: IPF AN SSSR, 1981) p. 117
  57. Purwins H.-G., Radehaus Ch., Berkemeier J. Z. Naturforsch. A 43 17 (1988)
  58. Kardell K., Radehaus Ch., Dokrnen R., Purwins H.-G. J. Appl. Phys. 64 6336 (1988)
  59. Nitzan A., Ross J. J. Chem. Phys. 59 241 (1973)
  60. Nitzan A., Ortoleva P., Ross J. J. Chem. Phys. 60 3134 (1974)
  61. Bunkin F. V., Kirichenko H. A., Luk’yanchik B. S., Morozov Yu. Yu. Kvantovaya Elektron. 10 2136 (1983); Bunkin F V et al. Sov. J. Quantum Electron. 13 1430 (1983)
  62. Polyakov S. V., Yakhno V. G. Fiz. Plazmy 6 383 (1980); Polyakov S V, Yakhno V G Sov. J. Plasma Phys. 6 211 (1980)
  63. Kuramoto Y., Tsuzuki T. Prog. Theor. Phys. 54 687 (1975); Kuramoto Y., Tsuzuki T. Prog. Theor. Phys. 55 356 (1976)
  64. Nitzan A., Ortoleva P. Phys. Rev. A 21 1735 (1980)
  65. Newell A. C., Whitehead J. A. J. Fluid Mech. 38 279 (1969)
  66. Segel L A J. Fluid Mech. 38 203 (1969)
  67. Siggia E, D., Zippelius A. Phys. Rev. A 26 1036 (1981)
  68. Swift L, Hohemberg R. S. Phys. Rev. A 15 319 (1977)
  69. Gertsberg V. S., Sivashinsky G. I. Prog. Theor. Phys. 66 1219 (1981)
  70. Malomed B A Z. Phys. 55 241 (1984)
  71. Malomed B. A. Nelineinye Volny: Struktury i Bifurkatsii (M.: Nauka, 1987) p. 251
  72. Gaponov-Grekhov A. V., Lomov A. S., Osipov G. V., Rabinovich M.I. Nelineinye Volny: Dinamika i Evolyutsiya (M.: Nauka, 1989) p. 61
  73. Akhromeeva T. S., Kurdyumov S. P., Malinetskii G. G., Samarskii A. A. Itogi Nauki i Tekhniki (Sovremennye problemy matematiki. Noveishie dostizheniya) Vol. 28 (M.: VINITI AN SSSR, 1987) p. 207
  74. Rabinovich M. I., Sushchik M. M. Usp. Fiz. Nauk 160 (1) 3 (1990); Rabinovich M I, Sushchik M M Sov. Phys. Usp. 33 1 (1990)
  75. Kerner B. S., Osipov V. V. Zh. Eksp. Teor. Fiz. 74 1675 (1978); Kerner B S, Osipov V V Sov. Phys. JETP 47 874 (1978)
  76. Kerner B. S., Osipov V. V. Fiz. Tekh. Poluprovodn. 13 721 (1979); Kerner B S, Osipov V V Sov. Phys. Semicond. 13 424 (1979)
  77. Kerner B. S., Osipov V. V. Zh. Eksp. Teor. Fiz. 79 2218 (1980); Kerner B S, Osipov V V Sov. Phys. JETP 52 1122 (1980)
  78. Kerner B. S., Osipov V. V. Dokl. Akad. Nauk SSSR 264 1366 (1982); Kerner B S, Osipov V V Sov. Phys. Dokl. 27 484 (1982)
  79. Kerner B. S., Osipov V. V. Mikroelektronika 14 389 (1985)
  80. Kerner B. S., Osipov V. V. Zh. Eksp. Teor. Fiz. 83 2201 (1982); Kerner B S, Osipov V V Sov. Phys. JETP 56 1275 (1982)
  81. Kerner B. S., Osipov V. V. Dokl. Akad. Nauk SSSR 270 1104 (1983); Kerner B S, Osipov V V Sov. Phys. Dokl. 28 485 (1983)
  82. Vasynyuk Z. I., Gafiichuk V. V., Kerner B. S., Osipov V. V. Fiz. Tverd. Tela 31 66 (1989); Vasynyuk Z I et al. Sov. Phys. Solid State 31 1875 (1989)
  83. Gafijchuk V. V., Kerner V. S., Osipov V. V., Vasyunyk Z.I. Proceedings of the Fourth International Workshop in Nonlinear and Turbulent Processes in Physics Vol. 1 (Kiev: Naukova Dumka) p. 107; Gafijchuk V. V., Kerner V. S., Osipov V. V., Vasyunyk Z.I. Noise in Physical Systems: Proceedings of the Tenth International Conference (Budapest, 1990) p. 609
  84. Vinoslavskii M. H. Fiz. Tverd. Tela 31 (8) 315 (1989); Vinoslavskii M N Sov. Phys. Solid State 31 1461 (1989); Vinoslavskil M. N., Kerner B. S., Osipov V. V., Sarbej O. G. J. Phys. Condens. Matter 2 686 (1990)
  85. Astrov Yu. A. "Generatsiya avtosolitonov pri dvoinoi inzhektsii v vysokoomnyi poluprovodnik" Preprint (L.: FTI AN SSSR, 1990)
  86. Berkemeier J., Dirksmeyer T., Klempt G., Purwins H.-G. Z. Phys. B 65 255 (1986); Purwins H.-G., Klempt G., Berkemeier Oyu Festkörperprobleme 27 27 (1987)
  87. a, Purwins H.-G., Radehaus. Ch. Neural And Synergetic Computers (Springer Series in Synergetics) Vol. 42 (Berlin: Springer-Verlag, 1988) p. 137; b, Purwins H-G, Radehaus Ch., Dirkmeyer T., Dohmen R., Schmeling R., Willsbrand H. Phys. Lett. A 136 480 (1989)
  88. Koga S., Kuramoto Y. Prog. Theor. Phys. 63 106 (1980)
  89. Chernavskii D. S., Ruijgrok Th. W. Biosystems 15 75 (1982)
  90. Kerner B. S., Kuznetsova E. M., Osipov V. V. Dokl. Akad. Nauk SSSR 277 1114 (1984); Kerner B S et al. Sov. Phys. Dokl. 29 644 (1984)
  91. Kerner B. S., Kuznetsova E. M., Osipov V. V. Mikroelektronika 13 407 (1984); Kerner B. S., Kuznetsova E. M., Osipov V. V. Mikroelektronika 13 456 (1984)
  92. Gierer A., Meinhardt H. Kybernetik 12 30 (1972)
  93. Meinhardt H., Gierer A. J. Cell. Sci. 15 321 (1974); Meinhardt H J. Cell. Sci. 23 117 (1977); Gierer A Naturwissenschaften 68 245 (1981)
  94. Balkarei Yu. I., Evtikhov M. G., Elinson M. I. Mikroelektronika 8 493 (1979); Balkarei Yu. I., Evtikhov M. G., Elinson M. I. Mikroelektronika 9 141 (1980); Balkarei Yu. I., Evtikhov M. G., Elinson M. I. Mikroelektronika 9 144 (1980); Balkarei Yu. I., Evtikhov M. G., Elinson M. I. Mikroelektronika 10 78 (1981)
  95. Balkarei Yu. I., Evtikhov M. G., Elinson M. I. Mikroelektronika 11 25 (1982); Balkarei Yu. I., Evtikhov M. G., Elinson M. I. Mikroelektronika 12 65 (1984); Balkarei Yu. I., Evtikhov M. G., Elinson M. I. Mikroelektronika 12 171 (1984)
  96. Elenin G. G., Krylov V. V., Polezhaev A. A., Chernavskii D. S. Dokl. Akad. Nauk SSSR 271 84 (1983); Elenin G G et al. Sov. Phys. Dokl. 28 542 (1983)
  97. Akhmetov A. A., Mints R. G. Pis’ma ZhTF 9 1306 (1983); Akhmetov A A, Mints R G Sov. Tech. Phys. Lett. 9 561 (1983)
  98. Dubitskii A. L., Kerner B. S., Osipov V. V. Fiz. Tekh. Poluprovodn. 20 1195 (1986); Dubitskii A L et al. Sov. Phys. Semicond. 20 755 (1986)
  99. Dubitskii A., Kerner B. S., Osipov V. V. Fiz. Tverd. Tela 28 (5) 1290 (1986); Dubitskii A L et al. Sov. Phys. Solid State 28 725 (1986)
  100. Gafiichuk V. V., Kerner B. S., Osipov V. V., Yuzhanin A. G. Pis’ma ZhTF 13 1299 (1987); Gafiichuk V V et al. Sov. Tech. Phys. Lett. 13 543 (1987)
  101. Gafiichuk V. V., Gashpar V. E., Kerner B. S., Osipov V. V. Fiz. Tekh. Poluprovodn. 22 1836 (1988); GafiTchuk V V et al. Sov. Phys. Semicond. 22 1161 (1988)
  102. a, Gafiichuk V. V., Kerner B. S., Lazurchak I. I., Osipov V. V. Mikroelektronika 15 180 (1986); b, Gafiichuk V. V., Kerner B. S., Lazurchak I. I., Osipov V. V. Mikroelektronika 19 (6) (1990)
  103. Osipov V. V., Lazurchak I. I., Gafiichuk V. V., Kerner B. S. Mikroelektronika 16 23 (1987)
  104. Gafiichuk V. V., Kerner B. S., Osipov V. V., Yuzhanin A. G. Fiz. Tekh. Poluprovodn. 22 2051 (1988); Gafiichuk V V et al. Sov. Phys. Semicond. 22 1298 (1988)
  105. Balkarei Yu. I., Evtikhov M. G., Elinson M. I. Zh. Tekh. Fiz. 57 209 (1987); Balkarei Yu I et al. Sov. Phys. Tech. Phys. 32 127 (1987); Balkarei Yu. I., Evtikhov M. G., Elinson M. I. Mikroelektronika 17 313 (1988)
  106. Balkarei Yu. I., Grigor’yants A. V., Rzhanoe Yu. A. Kvantovaya Elektron. 14 128 (1987); Balkarei Yu I et al. Sov. J. Quantum Electron. 17 72 (1987)
  107. Rozanov N. N., Khodova G. V. Opt. Spektr. 65 761 (1988); Opt. Spectrosc. (USSR) 65 449 (1988); Rosanov N N, Khodova G V J. Opt. Soc. Am. B 7 (6) (1990)
  108. Elenin G G, Lysak T M Mat. Modelirovanie 1 92 (1989)
  109. Grafiichuk V V, Kerner B S, Osipov V V, Yuzhanin A G "Statisticheskie avtosolitony i dissipativnye struktury v razogretoi elektronno-dyrochnoi plazme" Preprint (L’vov: IPPMM AN USSR, 1988)
  110. Gafiichuk V. V., Kerner B.S., Osipov V.V., Yuzhanin A.G. Zh. Tekh. Fiz. 60 8 (1990); Gafiichuk V V et al. Sov. Phys. Tech. Phys. 35 141 (1990)
  111. Gafiichuk V. V., Kerner B.S., Osipov V.V., Tyslyuk I.V. Fiz. Tverd. Tela 31 (8) 46 (1989); Gafiichuk V V et al. Sov. Phys. Solid State 31 1304 (1989)
  112. Gafiichuk V.V., Datsko B.I., Kerner B.S., Osipov V.V. Fiz. Tekh. Poluprovodn. 24 724 (1990); Gafiichuk V V et al. Sov. Phys. Semicond. 24 455 (1990)
  113. Gafiichuk V. V., Datsko B.I., Kerner B.S, Osipov V.V. Fiz. Tekh. Poluprovodn. 24 (7) (1990)
  114. Vasil’ev V.A. Termodinamika Biologicheskikh Protsessov (M.: Nauka, 1976) p. 198
  115. Kerner B S, Krinskii V I, Osipov V V Thermodynamics And Pattern Formation In Biology (New York: Walter de Gruyter, 1988) p. 265
  116. Talanov V I Dokl. Akad. Nauk SSSR 258 604 (1981); Talanov V I Sov. Phys. Dokl. 26 522 (1981)
  117. Gurevich A. V., Shvartsburg A.B. Nelineinaya Teoriya Rasprostraneniya Radiovoln v Ionosfere (M.: Nauka, 1973)
  118. Golant V. E., Zhilinskii A. P., Sakharov S. A. Osnovy Fiziki Plazmy (M.: Atomizdat, 1977)
  119. Bass F.G., Gurevich Yu. G. Goryachie Elektrony i Sil’nye Elektromagnitnye Volny v Plazme Poluprovodnikov i Gazovogo Razryada (M.: Nauka, 1975)
  120. Kerner B S, Osipov V V Self Organization By Nonlinear Irreversible Process (Springer Series in Synergertics) Vol. 33 (Berlin: Springer-Verlag, 1986) p. 118
  121. a, Hodgkin A L, Huxley A F J. Physiol. 116 449 (1952); Noble D J. Physiol. 160 317 (1962); b, Fitz-Hugh R Biophys. 1 445 (1961); Fitz-Hugh R Biophys. 2 11 (1962); Schwan H P (Ed.) Biological Engineering (New York: McGraw-Hill, 1969) p. 1; Nagumo I, Arimoto S, Yoshizawa S Proc. IRE 50 2061 (1962); Rinzel J, Keller J Biophys. 13 1313 (1973)
  122. a, Skott A. Volny v Aktivnykh i Nelineinykh Sredakh v Prilozhenii k Elektronike (M.: Sov. radio, 1977); Ostrovskii L.A., Yakhno V.G. Biofizika 20 489 (1975); b, Casten R G, Cohen H, Lagerstrom P A Quart. Appl. Math. 32 365 (1975)
  123. Winfree A T Sci. Am. 230 (6) 82 (1974); Winfree A T The Geometry Of Biological Time (New York: Springer-Verlag, 1980); Krinskii V.I., Agladze K.I. Dokl. Akad. Nauk SSSR 263 335 (1982); Krinskii V I, Agladze K I Sov. Phys. Dokl. 27 228 (1982); Krinskii V I, Agladze K I Nature 296 424 (1982); pertsov A M, Panfilov A Avtovolnovye Protsessy v Sistemakh s Diffuziei (Gor’kii: IPF AN SSSR, 1981) p. 77
  124. Zykov V S Modelirovanie Volnovykh Protsessov v Vozbudimykh Sredakh (M.: Nauka, 1984); Davydov V.A., Mikhailov A. S. Nelineinye Volny: Struktury i Bifurkatsii (M.: Nauka, 1987) p. 261
  125. Frolov A.A., Murav’ev I. P. Neitronnye Modeli Assotsiativnoi Pamyati (M.: Nauka, 1987)
  126. Vedenov A A Modelirovanie Elementov Myshleniya (M.: Nauka, 1988)
  127. Dubinin F. T. Optoelektronnye Modeli Odnorodnykh Sred (M.: Radio i svyaz’, 1984)
  128. Abraham R Lecture Notes In Mathematics Vol. 525 (Berlin: Springer-Verlag, 1976) p. 10
  129. Ferrano G, Hausler G Opt. Eng. 19 422 (1980)
  130. Crutchfield J P Physica D 10 229 (1984)
  131. Masterov A. V., Tolkov V.N., Yakhno V.G. Nelineinye Volny: Dinamika i Evolyutsiya (M.: Nauka, 1989) p. 166
  132. Masterov A.V., Rabinovich M.I., Tolkov V.N., Yakhno V.G. Kollektivnaya Dinamika Vozbuzhdenii i Strukturoobrazovanie v Biologicheskikh Tkanyakh (Gor’kii: IPF AN SSSR, 1988) p. 89
  133. Masterov A.V., Yakhno V.G. Kollektivnaya Dinamika Vozbuzhdenii i Strukturoobrazovanie v Biologicheskikh Tkanyakh (Gor’kii: IPF AN SSSR, 1988) p. 198
  134. Nicolis G, Auchmuty J F G Proc. Natl. Acad. Sci. USA 71 2748 (1974)
  135. Gafiichuk V. V. Avtoreferat kandidatskoi dissertatsii... kand. fiz.-mat. nauk (M.: MFTI, 1982)
  136. Malomed B A, Nepomnyashchy A A Proceedings of the Fourth International Workshop in Nonlinear and Turbulent Processes in Physics Vol. 2 (Kiev: Naukova Dumka) p. 291
  137. Petviashvili V.I., Sergeev A.M. Dokl. Akad. Nauk SSSR 276 1380 (1984); Petviashvili V I, Sergeev A M Sov. Phys. Dokl. 29 493 (1984)
  138. Kerner B.S. Mikroelektronika 5 257 (1976)
  139. Dubitskii A.L., Kerner B.S., Osipov V.V. Dokl. Akad. Nauk SSSR 308 857 (1989); Dubitskii A L et al. Sov. Phys. Dokl. 34 906 (1989)
  140. Kerner B. S, Osipov V.V. Pis’ma ZhETF 41 386 (1985); Kerner B S, Osipov V V JETPLett. 41 386 (1985)
  141. Kerner B.S, Osipov V.V. Dokl. Akad. Nauk SSSR 292 82 (1987); Kerner B S, Osipov V V Sov. Phys. Dokl. 32 43 (1987)
  142. Gurevich A. V., Mints R. G., Rakhmanov A. L. Fizika Kompozitnykh Sverkhprovodnikov (M.: Nauka, 1987)
  143. Kerner B.S., Osipov V.V., Shneider M.N. Radiotekhn. Elektron. 32 1909 (1987)
  144. Nitzan A, Ortoleva P, Deutch J, Ross J J. Chem. Phys. 61 1056 (1974)
  145. Balkarei Yu I, Sandomirskii V V Fiz. Tekh. Poluprovodn. 13 1006 (1979); Balkarei Yu I, Sandomirskii V V Sov. Phys. Semicond. 13 587 (1979)
  146. Zaitsev A A, Dzherpetov Kh A Zh. Eksp. Teor. Fiz. 24 516 (1953)
  147. Kerner B.S., Osipov V.V. Biofizika 27 137 (1982)
  148. Balkarei Yu.I., Nikulin M.G. Fiz. Tekh. Poluprovodn. 12 347 (1978); Balkarei Yu I, Nikulin M G Sov. Phys. Semicond. 12 201 (1978)
  149. Kerner B.S., Osipov V.V. Zh. Eksp. Teor. Fiz. 89 589 (1985); Kerner B S, Osipov V V Sov. Phys. JETP 62 337 (1985)
  150. Radehaus Ch, Kordell K, Baumann H, Jager D, Purwins H-G Z. Phys. B 67 515 (1987)
  151. Kerner B. S., Osipov V. B. Mikroelektronika 6 337 (1977)
  152. Thornton C G, Simmons C D IEEE Trans. Electron. Devices 5 6 (1958)
  153. Bergman F, Gertsner D Arch. Electron. Uebertragungstech. 17 467 (1963)
  154. Scarlett R M, Shockey W IEEE Intern. Conv. Rec. 3 3 (1963)
  155. Nechaev A M, Rubakha E A, Sinkevich V F Obzory Po Elektronnoi Tekhnike. Ser. 2. Vyp. 10 (M.: TsNII "Elektronika", 1978)
  156. Krein G D TIRI 50 2081 (1962); Crane H D Proc. IRE 50 2048 (1962)
  157. Komarovskikh K F, Murygin V N, Osipov V V, Stafeev V I Elektronnaya Tekhnika 6. Mikroelektronika (3) 11 (1967)
  158. Stafeev V.I, Komarovskikh K.F., Fursin G.I. Neiristornye i Drugie Funktsional’nye Skhemy s Obratnoi Svyaz’yu (M.: Radio i svyaz’, 1981)
  159. Berkovich S Ya Radiotekh. Elektron. 11 353 (1966)
  160. Kerner B S, Osipov V V Mikroelektronika 10 407 (1981)
  161. Ross D W Phys. Rev. 146 176 (1966)
  162. Blötekjar K, Weissglas P J. Appl. Phys. 39 1645 (1968)
  163. Gantmakher V F, Levinson I B Rasseyanie Nositelei Toka v Metallakh i Poluprovodnikakh (M.: Nauka, 1984)
  164. Kerner B S, Kozlov N A, Nechaev A M, Sinkevich V F Mikroelektronika 12 217 (1983); Kerner B S, Kozlov N A, Nechaev A M, Sinkevich V F Fiz. Tekh. Poluprovodn. 17 1931 (1983); Kerner B S et al. Sov. Phys. Semicond. 17 1235 (1983)
  165. Grafiichuk V V Fiz. Tverd. Tela 26 2230 (1984); Gafiichuk V V Sov. Phys. Solid State 26 1355 (1984)
  166. Celler G K, Robinson Mc D, Trimble L E, Lischner D J Appl Phys. Lett. 43 868 (1983)
  167. Allmen M, Von Lüthy W, Affolter K Appl. Phys. Lett. 33 824 (1978)
  168. Kiyak S. G., Bonchik A. Yu., Gafiichuk V. V., Yuzhanin A. G., Tyslyuk I.V. Izv. AN SSSR. Ser. Fiz. 52 1883 (1988)
  169. Sterword A V J. Appl. Phys. 27 911 (1956)
  170. Dubitskii A. L., Kerner B. S., Osipov V. V. Tezisy dokladov Vsesoyuznoi konferentsii "Fizicheskie i fiziko-khimicheskie osnovy mikroelektroniki" (Vil’nyus, 1987) p. 431
  171. Klyarfel’d B. Ya. Zh. Eksp. Teor. Fiz. 22 66 (1952)
  172. Kerner B.S., Osipov V.V. Mikroelektronika 12 512 (1983)
  173. Vasil’eva A.B., Butuzov V. F. Asimptoticheskie Razlozheniya Reshenii Singulyarnykh Uravnenii (M.: Nauka, 1973)
  174. Marri Dzh Nelineinye Differentsial’nye Uravneniya v Biologii. Lektsii o Modelyakh (M.: Mir, 1982)
  175. Naife A Vvedenie v Metody Vozmushchenii (M.: Mir, 1984)
  176. Ortoleva P., Ross I. J. Chem. Phys. 63 3398 (1975)
  177. Fife P C J. Chem. Phys. 64 554 (1976)
  178. Korn G., Korn T. Spravochnik Po Matematike (M.: Nauka, 1973)
  179. Ansel’m A I Vvedenie v Teoriyu Poluprovodnikov (M.: Nauka, 1978)
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