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 A.V. Gaponov-Grekhov 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 pdf (1.2 MB)
Fulltext is also available at DOI: 10.1070/PU1996v039n04ABEH000141
PACS: 87.10.+e
DOI: 10.1070/PU1996v039n04ABEH000141
URL: https://ufn.ru/en/articles/1996/4/b/
A1996UQ05700002
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 (157) ↓ Similar articles (20)

  1. Shakeel M, Liu X et al Communications In Nonlinear Science And Numerical Simulation 161 110120 (2026)
  2. Bhaumik A, Ghosh U et al Mater. Horiz. 13 (14) 6973 (2026)
  3. Qie X, Zang J et al Chaos: An Interdisciplinary Journal of Nonlinear Science 35 (4) (2025)
  4. Aranson I S, Malekhanov A I et al Radiophys Quantum El 68 (4) 321 (2025)
  5. Yao Ch, Zou W, Kurths Jürgen Chaos, Solitons & Fractals 200 117136 (2025)
  6. Di Palo E, Olm J M et al IEEE Trans. Control Netw. Syst. 11 (3) 1251 (2024)
  7. Herault J, Paez L et al Phys. Rev. E 110 (5) (2024)
  8. Remi T, Subha P A J. Phys. A: Math. Theor. 56 (34) 345701 (2023)
  9. Wang Ya, Zhang X, Liang S Nonlinear Dyn 111 (20) 19447 (2023)
  10. Kashchenko S, Mayorov V, Mayorova N Eur. Phys. J. Spec. Top. 232 (5) 509 (2023)
  11. Kongni S J, Nguefoue V et al Phys. Rev. E 108 (3) (2023)
  12. Bashkirtseva I A, Pisarchik A N, Ryashko L B Mathematics 11 (3) 597 (2023)
  13. Luo Z, Bo Y et al Journal of Applied Physics 131 (5) (2022)
  14. Glyzin S D, Kolesov A Yu Diff Equat 58 (7) 853 (2022)
  15. Bozhokin S V Studies In Computational Intelligence Vol. Advances in Neural Computation, Machine Learning, and Cognitive Research VWavelet Analysis of the Non-stationary Rose-Hindmarsh Model Describing Neural Activity1008 Chapter 20 (2022) p. 149
  16. Belykh I V, Daley K M, Belykh V N Radiophys Quantum El 64 (10) 700 (2022)
  17. Chen G IEEE/CAA J. Autom. Sinica 9 (4) 573 (2022)
  18. Sosa Raúl I, Zanette Dami?ln H Int. J. Bifurcation Chaos 31 (04) 2150056 (2021)
  19. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 6 (2021) p. 211
  20. Braga M H Materials 14 (9) 2398 (2021)
  21. Iqbal M Results In Control And Optimization 3 100016 (2021)
  22. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 1 (2021) p. 1
  23. Strelkova G I, Anishchenko V S ’pс’?’?kh’? ф’?’?’?ch’?с’?’?kh ’?’?у’? 190 (02) 160 (2020) [Strelkova G I, Anishchenko V S Phys.-Usp. 63 (2) 145 (2020)]
  24. Verichev N, Verichev S, Erofeev V Chaos, Synchronization and Structures in Dynamics of Systems with Cylindrical Phase Space Understanding Complex Systems Chapter 5 (2020) p. 109
  25. Mazurov M E Bull. Russ. Acad. Sci. Phys. 84 (3) 346 (2020)
  26. Cejnar P, Vy?lata Old?Tich ’? ’?р Sci Rep 10 (1) (2020)
  27. Kulminskiy D D, Ponomarenko V I et al Nonlinear Dyn 98 (1) 735 (2019)
  28. Budzinski R C, Boaretto B R R et al Communications In Nonlinear Science And Numerical Simulation 75 140 (2019)
  29. Glyzin S D Aut. Control Comp. Sci. 52 (7) 762 (2018)
  30. Klinshov V, Shchapin D et al Nonlinear Systems And Complexity Vol. Regularity and Stochasticity of Nonlinear Dynamical SystemsDynamics of Oscillatory Networks with Pulse Delayed Coupling21 Chapter 9 (2018) p. 219
  31. Ivanitskii G R Phys.-Usp. 61 (9) 871 (2018)
  32. Conde-Saavedra G, Ram?erez-Ávila Gonzalo Marcelo Chaos: An Interdisciplinary Journal of Nonlinear Science 28 (4) (2018)
  33. Contreras??BHern?lndez E, Ch?lvez D ’? ’?р The Journal Of Physiology 596 (9) 1747 (2018)
  34. Murray J D, Demirta?z Murat, Anticevic A Biological Psychiatry: Cognitive Neuroscience And Neuroimaging 3 (9) 777 (2018)
  35. Khobotov A G, Khil’ko A I, Tel’nykh A A Radiophys Quantum El 61 (1) 69 (2018)
  36. Iqbal M, Rehan M et al PLoS ONE 12 (5) e0176986 (2017)
  37. Liu X, Zhang K, Xie W-Ch IEEE Trans. Neural Netw. Learning Syst. 28 (5) 1055 (2017)
  38. Rubchinsky L L, Park Ch, Ahn S Nonlinear Systems And Complexity Vol. Advances in Dynamics, Patterns, CognitionDynamics of Intermittent Synchronization of Neural Activity20 Chapter 16 (2017) p. 263
  39. Bozhokin S V, Zharko S V et al Tech. Phys. 62 (6) 837 (2017)
  40. Reimbayev R, Zhao K, Belykh I Nonlinear Systems And Complexity Vol. Advances in Dynamics, Patterns, CognitionWhen Repulsive Inhibition Promotes Synchrony of Bursting Neurons: Help from the Enemy20 Chapter 11 (2017) p. 161
  41. Korkmaz N, Öztürk İsmail, Kılıç Recai Nonlinear Dyn 86 (3) 1841 (2016)
  42. Makarov V A, Calvo C et al IFAC-PapersOnLine 49 (14) 80 (2016)
  43. Wright T, Twaddle Ja et al Mathematical Biosciences 273 57 (2016)
  44. Guo D, Fu Y Q, Zheng B ChemPhysChem 17 (15) 2355 (2016)
  45. Selskii A, Makarov V A Regul. Chaot. Dyn. 21 (1) 97 (2016)
  46. Masulli P, Villa A E P SpringerPlus 5 (1) (2016)
  47. Prokin I S, Kazantsev V B Radiophys Quantum El 57 (10) 745 (2015)
  48. Cascallares G, S?lnchez Alejandro D et al Physica A: Statistical Mechanics And Its Applications 433 356 (2015)
  49. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 1 (2015) p. 1
  50. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 5 (2015) p. 177
  51. Kozma R, Wang Ju, Zeng Zh Springer Handbook of Computational Intelligence Chapter 33 (2015) p. 607
  52. Acedo L, Lamprianidou E et al Physica A: Statistical Mechanics And Its Applications 435 111 (2015)
  53. Ivanitskii G R, Deev A A, Khizhnyak E P ’pс’?’?kh’? ф’?’?’?ch’?с’?’?kh ’?’?у’? 184 (1) 43 (2014) [Ivanitskii G R, Deev A A, Khizhnyak E P Phys.-Usp. 57 (1) 37 (2014)]
  54. Heo M, Park J-K, Kim K Procedia Computer Science 29 2515 (2014)
  55. Mitra Ch, Ambika G, Banerjee S Chaos, Solitons & Fractals 69 188 (2014)
  56. Prado T d L, Lopes S R et al Phys. Rev. E 90 (3) (2014)
  57. Mesbah S, Moghtadaei M et al Chaos, Solitons & Fractals 65 20 (2014)
  58. Sedov A S, Medvednik R S, Raeva S N Hum Physiol 40 (1) 1 (2014)
  59. Wang Q, Zhang H, Chen G Eur. Phys. J. B 86 (7) (2013)
  60. Hu H, Pang L et al IJIS 03 (04) 145 (2013)
  61. Khobotov A G, I Kh A, I R V Radiophys Quantum El 56 (2) 95 (2013)
  62. Bozhokin S V, Suslova I M Tech. Phys. 58 (12) 1730 (2013)
  63. Klinshov V V, Nekorkin V I Phys.-Usp. 56 (12) 1217 (2013)
  64. Pavlov A N, Hramov A E et al ’pс’?’?kh’? ф’?’?’?ch’?с’?’?kh ’?’?у’? 182 (9) 905 (2012)
  65. Hu H, Shi Zh Lecture Notes In Computer Science Vol. Advances in Brain Inspired Cognitive SystemsThe Possibility of Using Simple Neuron Models to Design Brain-Like Computers7366 Chapter 41 (2012) p. 361
  66. Rubchinsky L L, Park Ch, Worth R M Nonlinear Dyn 68 (3) 329 (2012)
  67. McCULLEN N J, IVANCHENKO M V et al Int. J. Bifurcation Chaos 21 (09) 2467 (2011)
  68. Ibarz B, Casado J M, Sanju?ln M A F Physics Reports 501 (1-2) 1 (2011)
  69. Hu H, Shi Zh 2011 Seventh International Conference on Natural Computation, (2011) p. 475
  70. Wang Q, Chen G et al PLoS ONE 6 (1) e15851 (2011)
  71. Wang Q, Shi X, Chen G DCDS-B 15 (2) 607 (2011)
  72. Ovchinnikov A A, Hramov A E et al Tech. Phys. 56 (1) 1 (2011)
  73. Sedov A S, Medvednik R S, Raeva S N Neurosci Behav Physi 41 (9) 998 (2011)
  74. Rabinovich M I, Muezzinoglu M K Uspekhi Fizicheskikh Nauk 180 (4) 371 (2010)
  75. ’F’?’?’?’?’?’?’?ch Ya ’G, Kazanovich Y B Math.Biol.Bioinf. 5 (1) 43 (2010)
  76. Cao H, Ibarz B Phil. Trans. R. Soc. A. 368 (1930) 5071 (2010)
  77. Ivanitskii G R Uspekhi Fizicheskikh Nauk 180 (4) 337 (2010)
  78. Wang Q, Perc Matjaž ’? ’?р Physica A: Statistical Mechanics And Its Applications 389 (16) 3299 (2010)
  79. Koronovskii A A, Ovchinnikov A A, Hramov A E Phys. Wave Phen. 18 (4) 262 (2010)
  80. Li Ya-L, Li R 2010 Second WRI Global Congress on Intelligent Systems, (2010) p. 176
  81. Yang L, Jia Ya, Yi M 2010 Sixth International Conference on Natural Computation, (2010) p. 819
  82. Dmitriev A S, Ryzhov A I J. Commun. Technol. Electron. 55 (4) 429 (2010)
  83. Koronovskii A A, Moskalenko O I, Hramov A E Uspekhi Fizicheskikh Nauk 179 (12) 1281 (2009)
  84. Wang Q, Perc Matjaž ’? ’?р Phys. Rev. E 80 (2) (2009)
  85. LI YA-L, MA JU et al Int. J. Mod. Phys. C 20 (10) 1521 (2009)
  86. Yan-Long L, Jun M et al Chinese Phys. B 18 (10) 4598 (2009)
  87. Ivanitsky G R, Deev A A BIOPHYSICS 54 (3) 381 (2009)
  88. Skonzhenko L A, Krasichkov L V Tech. Phys. Lett. 35 (1) 5 (2009)
  89. Wang Q, Duan Zh et al Europhys. Lett. 83 (5) 50008 (2008)
  90. ’v’?’?’?р’?’?’? ’E ’R Uspekhi Fizicheskikh Nauk 178 (3) 313 (2008)
  91. Ch’?’? ’K, Chick D Math.Biol.Bioinf. 3 (1) 16 (2008)
  92. Li Ya-L, Ma Ju et al Chaos, Solitons & Fractals 37 (4) 1083 (2008)
  93. Han X, Lu Ju SCI CHINA SER F 50 (4) 615 (2007)
  94. Deng X, Geng H, Matache M T Biosystems 88 (1-2) 16 (2007)
  95. Ibarz B, Casado José Manuel, Sanju?ln Miguel A F Phys. Rev. E 75 (4) (2007)
  96. Cubero D, Casado-Pascual Jesús et al Phys. Rev. E 75 (6) (2007)
  97. Skonzhenko L A, Krasichkov L V Tech. Phys. Lett. 33 (6) 483 (2007)
  98. KUZNETSOV A S, FORTI G L, SHALFEEV V D Int. J. Bifurcation Chaos 16 (03) 741 (2006)
  99. Casado José M, Gómez Ordóñez José, Morillo M Phys. Rev. E 73 (1) (2006)
  100. Anishchenko V S, Astakhov V et al Nonlinear Dynamics of Chaotic and Stochastic Systems Springer Series In Synergetics Chapter 1 (2006) p. 1
  101. MATACHE M T Int. J. Mod. Phys. B 20 (08) 897 (2006)
  102. Volkov E I Radiophys Quantum Electron 48 (3) 212 (2005)
  103. WANG SH-JU, XU X-J et al Int. J. Mod. Phys. C 16 (12) 1841 (2005)
  104. Ivanchenko M V, Osipov G V, Shalfeev V D Radiophys Quantum Electron 48 (12) 934 (2005)
  105. Andreev K V, Krasichkov L V Radiophysics And Quantum Electronics 47 (7) 528 (2004)
  106. Ivanchenko M V, Osipov G V et al Phys. Rev. Lett. 93 (13) (2004)
  107. Casado José Manuel Physics Letters A 310 (5-6) 400 (2003)
  108. SHILNIKOV A L, RULKOV N F Int. J. Bifurcation Chaos 13 (11) 3325 (2003)
  109. Casado J M, Baltan?ls J P Phys. Rev. E 68 (6) (2003)
  110. Dodla R R V, Sen A, Johnston G L Communications In Nonlinear Science And Numerical Simulation 8 (3-4) 493 (2003)
  111. ZANETTE DAMIÁN H, MORELLI L G Int. J. Bifurcation Chaos 13 (04) 781 (2003)
  112. Aldana M, Coppersmith S, Kadanoff L P Perspectives and Problems in Nolinear Science Chapter 2 (2003) p. 23
  113. Andreev K V, Krasichkov L V Tech. Phys. Lett. 29 (2) 105 (2003)
  114. Mori T, Kai Sh Phys. Rev. Lett. 88 (21) (2002)
  115. Rulkov N F Phys. Rev. E 65 (4) (2002)
  116. Mikhailov A S, Calenbuhr V From Cells to Societies Springer Series In Synergetics Chapter 7 (2002) p. 155
  117. Huepe Cristi?ln, Aldana-Gonz?llez Maximino Journal Of Statistical Physics 108 (3-4) 527 (2002)
  118. Boccaletti S, Kurths J et al Physics Reports 366 (1-2) 1 (2002)
  119. Borisyuk G N, Borisyuk R M et al Uspekhi Fizicheskikh Nauk 172 (10) 1189 (2002)
  120. Rulkov N F, Afraimovich V S et al Phys. Rev. E 64 (1) (2001)
  121. Pazó Diego, Montejo N, Pérez-Muñuzuri Vicente Phys. Rev. E 63 (6) (2001)
  122. Schimansky-Geier L, Anishchenko V S, Neiman A Handbook Of Biological Physics Vol. Neuro-Informatics and Neural ModellingChapter 2 Phase synchronization: From periodic to chaotic and noisy4 (2001) p. 23
  123. Morelli L G, Zanette Dami?ln H Phys. Rev. E 63 (3) (2001)
  124. Rulkov N F Phys. Rev. Lett. 86 (1) 183 (2001)
  125. Vadivasova T E, Strelkova G I, Anishchenko V S Phys. Rev. E 63 (3) (2001)
  126. Sil’kis I G Neurosci Behav Physiol 31 (6) 573 (2001)
  127. Ivanitsky A M, Nikolaev A R, Ivanitsky G A International Journal Of Psychophysiology 42 (1) 35 (2001)
  128. Kuznetsov A S, Shalfeev V D Proceedings of the 2000 6th IEEE International Workshop on Cellular Neural Networks and their Applications (CNNA 2000, Cat. No.00TH8509), (2000) p. 419
  129. Giaquinta A, Argentina M, Velarde M G Journal Of Statistical Physics 101 (1-2) 665 (2000)
  130. Sanchez E, Matias M A, Perez-Munuzuri V IEEE Trans. Circuits Syst. I 47 (5) 644 (2000)
  131. Chernavskii D S Uspekhi Fizicheskikh Nauk 170 (2) 157 (2000)
  132. KOZLOV A K, SUSHCHIK M M et al Int. J. Bifurcation Chaos 09 (12) 2271 (1999)
  133. Zanette D H Europhys. Lett. 45 (4) 424 (1999)
  134. Mariño I P, Pérez-Muñuzuri V ’? ’?р Physica D: Nonlinear Phenomena 128 (2-4) 224 (1999)
  135. Hampton A, Zanette Dami?ln H Phys. Rev. Lett. 83 (11) 2179 (1999)
  136. SÁNCHEZ E, MATÍAS M A Int. J. Bifurcation Chaos 09 (12) 2335 (1999)
  137. Vanag V K Uspekhi Fizicheskikh Nauk 169 (5) 481 (1999)
  138. Sil’kis I G, Bogdanova O G Neurosci Behav Physiol 29 (3) 305 (1999)
  139. Rodr?eguez Francisco B, López Vicente Lecture Notes In Computer Science Vol. Foundations and Tools for Neural ModelingPeriodic and synchronic firing in an ensemble of identical stochastic units: Structural stability1606 Chapter 39 (1999) p. 367
  140. Ivanitsky A M, Nikolaev A R, Ivanitsky G A Modern Techniques in Neuroscience Research Chapter 35 (1999) p. 971
  141. Zanette D H, Mikhailov A S Phys. Rev. E 58 (1) 872 (1998)
  142. Bazhenov M, Huerta R et al Physica D: Nonlinear Phenomena 116 (3-4) 392 (1998)
  143. Nekorkin V I, Makarov V A, Velarde M G Phys. Rev. E 58 (5) 5742 (1998)
  144. Nekorkin V I, Kazantsev V B et al Phys. Rev. E 57 (3) 3344 (1998)
  145. S?lnchez E, Mat?eas M A Phys. Rev. E 57 (5) 6184 (1998)
  146. Makarenko V, Llin?ls Rodolfo Proc. Natl. Acad. Sci. U.S.A. 95 (26) 15747 (1998)
  147. Vol. MMET Conference Proceedings. 1998 International Conference on Mathematical Methods in Electromagnetic Theory. MMET 98 (Cat. No.98EX114)Stochastic model of interaction of electromagnetic waves with random active mediaV.G.Spitsyn2 (1998) p. 866
  148. Sil’kis I G, Bogdanova O G Neurosci Behav Physiol 28 (6) 645 (1998)
  149. Belykh I V Radiophys Quantum Electron 41 (12) 1066 (1998)
  150. Kazantsev V B, Nekorkin I, Velarde M G Radiophys Quantum Electron 41 (12) 1101 (1998)
  151. Zanette D H, Mikhailov A S Physics Letters A 235 (2) 135 (1997)
  152. Rabinovich M I, Abarbanel H D I et al IEEE Trans. Circuits Syst. I 44 (10) 997 (1997)
  153. Battogtokh D, Hildebrand M et al Physics Reports 288 (1-6) 435 (1997)
  154. Zanette D H Phys. Rev. E 55 (5) 5315 (1997)
  155. Vanag V K J. Phys. Chem. A 101 (38) 7074 (1997)
  156. Vol. 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96Intelligent identification and control of chaotic dynamicsGuanrong Chen3 (1996) p. 5
  157. Rabinovich M I Radiophys Quantum Electron 39 (6) 502 (1996)

© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions