Issues

 / 

1996

 / 

April

  

Reviews of topical problems


Synchronisation in neural networks

 a,  b,  a,  b,  a,  b,  b
a Department of Physics, University of California, Santa Barbara, CA, USA
b Federal Research Center Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation

The construction of a dynamical theory of neural networks has been a goal of physicists, mathematicians and biologists for many years now. Experimental breakthroughs in modern neurobiology have allowed researchers to approach this goal. Significant advances have been made for small neural networks, which are generators of the rhythmic activities of living organisms. The subject of the present review is the problem of synchronisation, one of the major aspects of the dynamical theory. It is shown that synchronisation plays a key role in the activity of both minimal neural networks (neural pair) and neural assemblies with a large number of elements (cortex).

Fulltext is available at IOP
PACS: 87.10.+e
DOI: 10.1070/PU1996v039n04ABEH000141
URL: https://ufn.ru/en/articles/1996/4/b/
Citation: Abarbanel H D, Rabinovich M I, Selverston A, Bazhenov M V, Huerta R, Sushchik M M, Rubchinskii L L "Synchronisation in neural networks" Phys. Usp. 39 337–362 (1996)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Абарбанель Г Д, Рабинович М И, Селверстон А, Баженов М В, Хуэрта Р, Сущик М М, Рубчинский Л Л «Синхронизация в нейронных ансамблях» УФН 166 363–390 (1996); DOI: 10.3367/UFNr.0166.199604b.0363

References (149) ↓ Cited by (138) Similar articles (20)

  1. Huygens H Tri Memuara po Mekhanike (Three Memoirs in Mechanics, Ed. by K Baumgart, Translated into Russian, Moscow: Academy of Sciences of USSR Publishing House, 1951)
  2. Rayleigh Teoriya Zvuka (Theory of Sound) Vol. 1, 2 (Translated into Russian, Moscow: Gostekhizdat, 1940, 1944)
  3. Van der Pol B Nelineinaya Teoriya Electricheskikh Kolebanii (Nonlinear Theory of Electrical Oscillations, Translated into Russian, Moscow: Svyaz’izdat, 1935)
  4. Andronov A A, Vitt A A, Haikin S E Teoriya Kolebanii (Theory of Oscillations, Translated into Russian, Moscow: Fizmatgiz, 1959)
  5. Hedley P, Beasley M R, Wiesenfeld K Phys. Rev. B 38 8712 (1988)
  6. Arnol’d V I et al., in Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya (Contemporary Problems of Mathematics. Basic Directions) Vol. 5 (Ed. V I Arnol’d, Moscow: VINITI, 1986)
  7. Afraimovich V S, Verichev N N, Rabinovich M I Izv. Vyssh. Uchebn. Zaved. Radiofiz. 29 1050 (1986)
  8. Szekely G Acta Phys. Acad. Hyng. 27 285 (1965)
  9. Afraimovich V S, Reiman A M, in Nelineinye Volny. Dinamica i Evolutsiya (Nonlinear Waves. Dynamics and Evolution, Ed. A V Gaponov-Grekhov, M I Rabinovich, Moscow: Nauka, 1989) p. 238
  10. Aranson I S, Reiman A M, Shekhov B G Ibid., p. 262
  11. Abarbanel H D I et al. Rev. Mod. Phys. 65 1331 (1993)
  12. Shepherd G M Neurobiology (Oxford: Oxford Univ. Press, 1994)
  13. Buchholtz F et al. J. Neurophysiol. 67 332 (1992)
  14. Hodgkin A L, Huxley A F J. Physiol. (London) 117 500 (1952)
  15. Morris C, Lecar H Biophys. J. 35 193 (1981)
  16. Hayashi H, Ishizuka S J. Theor. Biol. 156 269 (1992)
  17. Abarbanel H D I et al. Biol. Cybern. (1996, to be published)
  18. Chay T R Physica D 16 233 (1985)
  19. Hindmarsh J L, Rose R M Proc. R. Soc. London. Ser. B 221 87 (1984)
  20. Wilson H, Cowan J Kybernetic 13 55 (1973)
  21. Ermentrout G B, Kopell N SIAM J. Math. Anal. 15 215 (1984)
  22. Borisyuk G I et al. Matematisheskoe Modelirovanie 4 3 (1991)
  23. Cuffler S, Nikkols J Ot Neirona k Mozgu (From Neuron to Brain, Translated into Russian, Moscow: Mir, 1979)
  24. Shapovalov A I, Shiryaev B I Peredacha Signalov v Mezhneironnykh Sinapsakh (Transmission of Signals in Synapses, Leningrad: Nauka, 1987)
  25. Agmon-Snir H, Segev I J. Neurophysiol. 70 (5) 2066 (1993)
  26. Kalil R E et al. Nature (London) 323 156 (1986)
  27. Voronin L L Synaptic Modifications and Memory (Berlin, 1993)
  28. Byzov A L, Shura-Bura T M Vision Res. 26 33 (1986)
  29. Matyushkin D P Obratnye Svyazi v Sinapse (Feed-back in Synapse, Moscow, 1989)
  30. Hebb D O The Organization of Behaviour (New York: Wiley, 1949)
  31. Hertz J, Krogh A, Palmer R G Itroduction to the Theory of Neural Computation (Redwood city: Addison Welsey, 1991)
  32. Hopfield J J Proc. Natl. Acad. Sci. USA 79 2554 (1982)
  33. Hopfield J J Phys. Today 40-46 (1994)
  34. Harris-Worrick R M, Marder E, Selverston A I Dynamic Biological Networks (Cambridge: MIT Press, 1992)
  35. Arshavsky Yu I et al. TINS 16 227 (1993)
  36. Katz P S, Getting P A, Frost W N Nature (London) 367 723 (1994)
  37. Huerta P T, Lisman J E Nature (London) 364 723 (1993)
  38. Schuman E M, Madison D V Science 263 532 (1994)
  39. Mpitos G J et al. Brain Res. Bull. 21 529 (1988)
  40. Selverston A et al. (to be published)
  41. Fujisaka H, Yamada T Prog. Theor. Phys. 69 32 (1983)
  42. Rulkov N F et al. Int. J. Bif. Chaos 2 669 (1992)
  43. Arshavsky Yu I et al. (to be published).
  44. Delcomyn F Science 210 492 (1980)
  45. Grillner S Science 228 143 (1985)
  46. Rowell C H F Semin. Neurosci. 5 59 (1993)
  47. Collins J J, Stewart I N J. Nonlinear Sci. 3 349 (1993)
  48. Grillner S, Kashin S, in Neural Control of Locomotion (Eds R Herman, S Grillner, P Stein, L Stuart, New York: Plenum Press, 1976) p. 181
  49. Grillner S et al. Semin. Neurosci. 5 17 (1993)
  50. Grillner S Exp. Brain. Res. 20 459 (1974)
  51. Wallen P, Williams T L J. Physiol. (London) 347 225 (1984)
  52. Williams T L et al. J. Exp. Biol. 143 559 (1989)
  53. Timstall M J, Roberts A Pros. R. Soc. London. Ser. B 244 27 (1991)
  54. Paul D H, Mulloney D J. Neurophysiol. 54 28 (1985)
  55. Sigvardt K A Semin. Neurosci. 5 3 (1993)
  56. McClellan A D, Sigvardt K A J. Neurosci. 8 133 (1988)
  57. Rovainen C J. Neurophysiol. 54 959 (1985)
  58. Rabinovich M I, Trubetskov D I Oscillations and Waves in Linear and Nonlinear Systems (Dorderecht, Boston, London: Kluwer Academic Publ., 1989)
  59. Cohen A H, Holmes P J, Rand R H J. Math. Biol. 13 345 (1982)
  60. Williams T L Neural Computation 4 546 (1992)
  61. Grillner S et al. Annu. Rev. Neurosci. 14 169 (1981)
  62. Weeks J C J. Neurophysiol. 45 698 (1981)
  63. Hashemzadeh-Gargari H, Friesen W O Comp. Biochem. Physiol. 94C 295 (1989)
  64. Friesen W O, Pearce R A Semin. Neurosci. 5 41 (1993)
  65. Grillner S, Perret C, Zangger P Brain. Res. 109 225 (1976)
  66. Grillner S, Wallen P Brain. Res. 127 291 (1977)
  67. Stein P S G J. Comp. Physiol. 124 203 (1978)
  68. Kulagin A S, Shik M L Biophys. 15 171 (1970)
  69. Shik M L, Orlovsky G N Physiol. Rev. 56 465 (1976)
  70. Forrsberg H et al. Acta Physiol. Scand. 100 283 (1980)
  71. Collins J J, Stewart I N Biol. Cybern. 68 287 (1993)
  72. Kuramoto Y Chemical Oscillations Waves and Turbulence (Berlin: Springer, 1984)
  73. Kuramoto Y Progr. Theor. Phys. Suppl. 79 223 (1984)
  74. Cohen A H TINS 15 434 (1992)
  75. Williams T L et al. J. Neurophysiol. 64 862 (1990)
  76. Cohen A H J. Comp. Physiol. A 160 181 (1987)
  77. Ermentrout G B, Kopell N SIAM J. Appl. Math. 54 478 (1994)
  78. Nishii J, Uno Y, Suzuki R Biol. Cybern. 72 1 (1994)
  79. Osovets S M et al. Usp. Fiz. Nauk 141 103 (1983) [Sov. Phys. Usp. 26 801 (1983)]
  80. Schuster H G, Wagner P Biol. Cybern. 64 77 (1990)
  81. Von der Malsburg C Internal Report 81-2, Abteilung fPr Neurobiologie (Goettingen: MPI fPr Biophysikalische Chemie, 1981)
  82. Von der Malsburg C, Schneider W Biol. Cybern. 54 29 (1986)
  83. Livingstone M, Hubel D Science 240 740 (1988)
  84. Zeki S, Shipp S Nature (London) 335 311 (1988)
  85. Eckhorn R et al. Biol. Cybern. 60 121 (1988)
  86. Gray C M, Singer W Proc. Natl. Acad. Sci. USA 86 1698 (1989)
  87. Engel A K et al. Eur. J. Neurosci. 2 588 (1990)
  88. Gray C M et al. Ibid., p. 607
  89. Gray C M et al. Nature (London) 338 334 (1989)
  90. Principles of Neural Science (Eds E R Kandel, J H Schwarz) 2nd edition (New York, Amsterdam, Oxford: Elsevier, 1985)
  91. Engel A K, Koenig P, Singer W Proc. Natl. Acad. Sci. USA 88 9136 (1991)
  92. Koenig P et al. Neural Comp. 7 469 (1995)
  93. Nelson J I et al. Visual Neurosci. 9 21 (1992)
  94. Koenig P et al. Eur. J. Neurosci. 5 501 (1993)
  95. Ts’o D Y, Gilbert C D J. Neurosci. 8 1712 (1988)
  96. Krueger J, Aiple F J. Neurophysiol. 60 798 (1988)
  97. Engel A K et al. Proc. Natl. Acad. Sci. USA 88 6048 (1991)
  98. Engel A K et al. Science 252 1177 (1991)
  99. Chawanya T et al. Biol. Cybern. 68 483 (1993)
  100. Knight B W J. Gen. Physiol. 59 734 (1972)
  101. Peskin C S Mathematical Aspects of Heart Physiology (New York: Courant. Inst. of Math. Sci. Publication, 1975) p. 268
  102. Koenig P, Schillen T B Neural Comp. 3 155 (1991)
  103. Gerstner W Phys. Rev. E 51 738 (1995)
  104. Schillen T B, Koenig P Neural Comp. 3 167 (1991)
  105. Sporns O et al. Neurobiol. 86 7265 (1989)
  106. Grannan E R, Kleinfeld D, Sompolinsky H Neural Comp. 5 550 (1993)
  107. Terman D, Wang D L Physica D 81 148 (1995)
  108. Von der Malsburg C, Buhmann J Biol. Cybern. 67 233 (1992)
  109. Horn D, Sagi D, Usher M Neural Comp. 3 510 (1991)
  110. Meinhardt H, Koch A J Rev. Mod. Phys. 66 1481 (1994)
  111. Ivanitskii G R, Medvinskii A B, Tsyganov M A Usp. Fiz. Nauk 164 1041 (1994) [Phys. Usp. 37 961 (1994)]
  112. Vasiev B N, Hogeweg P, Parfilov A V Phys. Rev. Lett. 73 3173 (1994)
  113. Rabinovich M I, Sushchik M M Usp. Fiz. Nauk 160 (1) 3 (1990) [Sov. Phys. Usp. 33 1 (1990)]
  114. Gaponov-Grekhov A V, Rabinovich M I Nonlinearity in Action (Heidelberg: Springer, 1991)
  115. Bailly C H, Kandel E R Annu. Rev. Physiol. 55 397 (1993)
  116. Wang D, Buhmann J, von der Malsburg C Neural Comp. 2 94 (1990)
  117. Baird B, Eeckman F, in Associative Neural Memories. Theory and Implemenation (Ed. M H Hassoun, New York, Oxford: Oxford Univ. Press, 1993) p. 135
  118. Hopfield J J, Tank D W Science 233 625 (1986)
  119. Sompolinsky H, Tsodyks M Neural Comp. 6 642 (1994)
  120. Fukai T Biol. Cybern. 71 215 (1994)
  121. Rosenblueth A, Cannon W B Am. J. Physiol. 135 349 (1942)
  122. Burns D B The Mammalian Cerebral Cortex (London: Arnold, 1958)
  123. Winfree A T When Time Breaks Down (Princeton, New Jersey: Princeton Univ. Press, 1987)
  124. Loskutov A Yu, Mikhailov A S Vvedenie v Sinergetiku (Introduction to Synergetics, Moscow: Nauka, 1990)
  125. Davidenko J M, Kent P, Jalife J Physica D 49 182 (1991)
  126. Downar E et al. J. Am. Coll. Cardiol. 4 703 (1984)
  127. Gorelova N A, Bures J J. Neurobiol. 14 353 (1983)
  128. Shibata M, Bures J J. Neurophys. 35 381 (1972); 5 107 (1974)
  129. Paullet J E, Ermentrout G B SIAM J. Appl. Math. 54 1720 (1994)
  130. Kaplan D T et al. Math. Biosci. 90 19 (1988)
  131. Chu P H, Milton J G, Cowan J D Int. J. Bif. Chaos 4 237 (1994)
  132. Geisler C D, Goldberg J M Biophysical J. 6 53 (1966)
  133. Sholl D A The Organization of the Cerebral Cortex (London: Methuen, 1956)
  134. Destexhe A Phys. Rev. E 50 1594 (1994)
  135. Coullet P, Gil L, Lega J Physica D 37 91 (1989); Phys. Rev. Lett. 62 1619 (1989)
  136. Cowan J D, in Proc. of the founding workshop of the Santa Fe Institute, Santa Fe, New Mexico (Addison: Wesley, 1987) p. 123
  137. Turchin V Fenomen Nauki (Phenomenon of Science, Moscow: Nauka, 1993)
  138. Hansel D, Mato G, Meunier C Neural Comp. 7 307 (1995)
  139. Connar J A, Walter D, McKown Biophys. 18 81 (1977)
  140. Skinner F K, Turrigiano G G, Marder E Biol. Cybern. 69 375 (1993)
  141. Ermentrout B, Kopell N Neural Comp. 6 225 (1994)
  142. Chay T R, Fan Y S, Lee Y S Int. J. Bif. Chaos 5 595 (1995)
  143. Chay T R Biol. Cybern. 63 15 (1990)
  144. Golowasch J, Marder E J Neurophys. 67 318 (1992)
  145. Golomb D, Guckenheimer J, Gueron S Biol. Cybern. 69 129 (1993)
  146. Stein R B et al. Kybernetic 15 1 (1974)
  147. FitzHygh R Biophys. J. 1 445 (1961)
  148. Nagumo J, Arimoto S, Yoshizawa S Proc. IRE 50 2061 (1962)
  149. Bay J S, Hemani H IEE Trans. Biomed. Eng. 34 297 (1987)

© 1918–2021 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions