RSS feeds
РусскийEnglish
Issue 12, 2025
Volume year page
Issues Authors PACS Subscription For authors

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 (154) ↓ Similar articles (20)

  1. Yao Ch, Zou W, Kurths J Chaos, Solitons & Fractals 200 117136 (2025)
  2. Qie X, Zang J et al Chaos: An Interdisciplinary Journal of Nonlinear Science 35 (4) (2025)
  3. Di Palo E, Olm J M et al IEEE Trans. Control Netw. Syst. 11 (3) 1251 (2024)
  4. Herault J, Paez L et al Phys. Rev. E 110 (5) (2024)
  5. Wang Ya, Zhang X, Liang S Nonlinear Dyn 111 (20) 19447 (2023)
  6. Kongni S J, Nguefoue V et al Phys. Rev. E 108 (3) (2023)
  7. Remi T, Subha P A J. Phys. A: Math. Theor. 56 (34) 345701 (2023)
  8. Kashchenko S, Mayorov V, Mayorova N Eur. Phys. J. Spec. Top. 232 (5) 509 (2023)
  9. Bashkirtseva I A, Pisarchik A N, Ryashko L B Mathematics 11 (3) 597 (2023)
  10. 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
  11. Chen G IEEE/CAA J. Autom. Sinica 9 (4) 573 (2022)
  12. Glyzin S D, Kolesov A Yu Diff Equat 58 (7) 853 (2022)
  13. Luo Z, Bo Y et al Journal of Applied Physics 131 (5) (2022)
  14. Belykh I V, Daley K M, Belykh V N Radiophys Quantum El 64 (10) 700 (2022)
  15. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 6 (2021) p. 211
  16. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 1 (2021) p. 1
  17. Iqbal M Results In Control And Optimization 3 100016 (2021)
  18. Braga M H Materials 14 (9) 2398 (2021)
  19. Sosa R I, Zanette D H Int. J. Bifurcation Chaos 31 (04) 2150056 (2021)
  20. Strelkova G I, Anishchenko V S Uspekhi Fizicheskikh Nauk 190 (02) 160 (2020) [Strelkova G I, Anishchenko V S Phys.-Usp. 63 (2) 145 (2020)]
  21. Cejnar P, Vyšata Oldřich et al Sci Rep 10 (1) (2020)
  22. 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
  23. Mazurov M E Bull. Russ. Acad. Sci. Phys. 84 (3) 346 (2020)
  24. Budzinski R C, Boaretto B R R et al Communications In Nonlinear Science And Numerical Simulation 75 140 (2019)
  25. Kulminskiy D D, Ponomarenko V I et al Nonlinear Dyn 98 (1) 735 (2019)
  26. Murray J D, Demirtaş M, Anticevic A Biological Psychiatry: Cognitive Neuroscience And Neuroimaging 3 (9) 777 (2018)
  27. 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
  28. Contreras‐Hernández E, Chávez D et al The Journal Of Physiology 596 (9) 1747 (2018)
  29. Ivanitskii G R Phys.-Usp. 61 (9) 871 (2018)
  30. Glyzin S D Aut. Control Comp. Sci. 52 (7) 762 (2018)
  31. Conde-Saavedra G, Ramírez-Ávila G M Chaos: An Interdisciplinary Journal of Nonlinear Science 28 (4) (2018)
  32. Khobotov A G, Khil’ko A I, Tel’nykh A A Radiophys Quantum El 61 (1) 69 (2018)
  33. Bozhokin S V, Zharko S V et al Tech. Phys. 62 (6) 837 (2017)
  34. Iqbal M, Rehan M et al PLoS ONE 12 (5) e0176986 (2017)
  35. 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
  36. 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
  37. Liu X, Zhang K, Xie W-Ch IEEE Trans. Neural Netw. Learning Syst. 28 (5) 1055 (2017)
  38. Korkmaz N, Öztürk İ, Kılıç R Nonlinear Dyn 86 (3) 1841 (2016)
  39. Makarov V A, Calvo C et al IFAC-PapersOnLine 49 (14) 80 (2016)
  40. Selskii A, Makarov V A Regul. Chaot. Dyn. 21 (1) 97 (2016)
  41. Masulli P, Villa A E P SpringerPlus 5 (1) (2016)
  42. Guo D, Fu Y Q, Zheng B ChemPhysChem 17 (15) 2355 (2016)
  43. Wright T, Twaddle Ja et al Mathematical Biosciences 273 57 (2016)
  44. Cascallares G, Sánchez A D et al Physica A: Statistical Mechanics And Its Applications 433 356 (2015)
  45. Prokin I S, Kazantsev V B Radiophys Quantum El 57 (10) 745 (2015)
  46. Acedo L, Lamprianidou E et al Physica A: Statistical Mechanics And Its Applications 435 111 (2015)
  47. Kozma R, Wang Ju, Zeng Zh Springer Handbook of Computational Intelligence Chapter 33 (2015) p. 607
  48. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 1 (2015) p. 1
  49. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 5 (2015) p. 177
  50. Mitra Ch, Ambika G, Banerjee S Chaos, Solitons & Fractals 69 188 (2014)
  51. Prado T de L, Lopes S R et al Phys. Rev. E 90 (3) (2014)
  52. Mesbah S, Moghtadaei M et al Chaos, Solitons & Fractals 65 20 (2014)
  53. Sedov A S, Medvednik R S, Raeva S N Hum Physiol 40 (1) 1 (2014)
  54. Ivanitskii G R, Deev A A, Khizhnyak E P Uspekhi Fizicheskikh Nauk 184 (1) 43 (2014) [Ivanitskii G R, Deev A A, Khizhnyak E P Phys.-Usp. 57 (1) 37 (2014)]
  55. Heo M, Park J-K, Kim K Procedia Computer Science 29 2515 (2014)
  56. Hu H, Pang L et al IJIS 03 (04) 145 (2013)
  57. Wang Q, Zhang H, Chen G Eur. Phys. J. B 86 (7) (2013)
  58. Khobotov A G, I Kh A, I R V Radiophys Quantum El 56 (2) 95 (2013)
  59. Bozhokin S V, Suslova I M Tech. Phys. 58 (12) 1730 (2013)
  60. Klinshov V V, Nekorkin V I Phys.-Usp. 56 (12) 1217 (2013)
  61. Rubchinsky L L, Park Ch, Worth R M Nonlinear Dyn 68 (3) 329 (2012)
  62. Pavlov A N, Hramov A E et al Uspekhi Fizicheskikh Nauk 182 (9) 905 (2012)
  63. 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
  64. Sedov A S, Medvednik R S, Raeva S N Neurosci Behav Physi 41 (9) 998 (2011)
  65. Ovchinnikov A A, Hramov A E et al Tech. Phys. 56 (1) 1 (2011)
  66. Wang Q, Shi X, Chen G Discrete & Continuous Dynamical Systems - B 16 (2) 607 (2011)
  67. McCULLEN N J, IVANCHENKO M V et al Int. J. Bifurcation Chaos 21 (09) 2467 (2011)
  68. Hu H, Shi Zh 2011 Seventh International Conference on Natural Computation, (2011) p. 475
  69. Wang Q, Chen G et al PLoS ONE 6 (1) e15851 (2011)
  70. Ibarz B, Casado J M, Sanjuán M A F Physics Reports 501 (1-2) 1 (2011)
  71. Rabinovich M I, Muezzinoglu M K Uspekhi Fizicheskikh Nauk 180 (4) 371 (2010)
  72. Li Ya-L, Li R 2010 Second WRI Global Congress on Intelligent Systems, (2010) p. 176
  73. Ivanitskii G R Uspekhi Fizicheskikh Nauk 180 (4) 337 (2010)
  74. Cao H, Ibarz B Phil. Trans. R. Soc. A. 368 (1930) 5071 (2010)
  75. Kazanovich Ya B, Kazanovich Y B Math.Biol.Bioinf. 5 (1) 43 (2010)
  76. Dmitriev A S, Ryzhov A I J. Commun. Technol. Electron. 55 (4) 429 (2010)
  77. Wang Q, Perc M et al Physica A: Statistical Mechanics And Its Applications 389 (16) 3299 (2010)
  78. Koronovskii A A, Ovchinnikov A A, Hramov A E Phys. Wave Phen. 18 (4) 262 (2010)
  79. Yang L, Jia Ya, Yi M 2010 Sixth International Conference on Natural Computation, (2010) p. 819
  80. Ivanitsky G R, Deev A A BIOPHYSICS 54 (3) 381 (2009)
  81. Yan-Long L, Jun M et al Chinese Phys. B 18 (10) 4598 (2009)
  82. LI YAN-LONG, MA JUN et al Int. J. Mod. Phys. C 20 (10) 1521 (2009)
  83. Skonzhenko L A, Krasichkov L V Tech. Phys. Lett. 35 (1) 5 (2009)
  84. Koronovskii A A, Moskalenko O I, Hramov A E Uspekhi Fizicheskikh Nauk 179 (12) 1281 (2009)
  85. Wang Q, Perc M et al Phys. Rev. E 80 (2) (2009)
  86. Li Ya-L, Ma Ju et al Chaos, Solitons & Fractals 37 (4) 1083 (2008)
  87. Chik D, Chick D Math.Biol.Bioinf. 3 (1) 16 (2008)
  88. Nekorkin V I Uspekhi Fizicheskikh Nauk 178 (3) 313 (2008)
  89. Wang Q, Duan Zh et al Europhys. Lett. 83 (5) 50008 (2008)
  90. Skonzhenko L A, Krasichkov L V Tech. Phys. Lett. 33 (6) 483 (2007)
  91. Deng X, Geng H, Matache M T Biosystems 88 (1-2) 16 (2007)
  92. Han XiuPing, Lu JunAn SCI CHINA SER F 50 (4) 615 (2007)
  93. Ibarz B, Casado J M, Sanjuán M A F Phys. Rev. E 75 (4) (2007)
  94. Cubero D, Casado-Pascual Je et al Phys. Rev. E 75 (6) (2007)
  95. Casado J M, Gómez O J, Morillo M Phys. Rev. E 73 (1) (2006)
  96. Anishchenko V S, Astakhov V et al Nonlinear Dynamics of Chaotic and Stochastic Systems Springer Series In Synergetics Chapter 1 (2006) p. 1
  97. MATACHE MIHAELA T Int. J. Mod. Phys. B 20 (08) 897 (2006)
  98. KUZNETSOV A S, FORTI G L, SHALFEEV V D Int. J. Bifurcation Chaos 16 (03) 741 (2006)
  99. Volkov E I Radiophys Quantum Electron 48 (3) 212 (2005)
  100. Ivanchenko M V, Osipov G V, Shalfeev V D Radiophys Quantum Electron 48 (12) 934 (2005)
  101. WANG SHENG-JUN, XU XIN-JIAN et al Int. J. Mod. Phys. C 16 (12) 1841 (2005)
  102. Andreev K V, Krasichkov L V Radiophysics And Quantum Electronics 47 (7) 528 (2004)
  103. Ivanchenko M V, Osipov G V et al Phys. Rev. Lett. 93 (13) (2004)
  104. Casado J M Physics Letters A 310 (5-6) 400 (2003)
  105. Aldana M, Coppersmith S, Kadanoff L P Perspectives and Problems in Nolinear Science Chapter 2 (2003) p. 23
  106. Andreev K V, Krasichkov L V Tech. Phys. Lett. 29 (2) 105 (2003)
  107. SHILNIKOV ANDREY L, RULKOV NIKOLAI F Int. J. Bifurcation Chaos 13 (11) 3325 (2003)
  108. ZANETTE DAMIÁN H, MORELLI LUIS G Int. J. Bifurcation Chaos 13 (04) 781 (2003)
  109. Dodla R R V, Sen A, Johnston G L Communications In Nonlinear Science And Numerical Simulation 8 (3-4) 493 (2003)
  110. Casado J M, Baltanás J P Phys. Rev. E 68 (6) (2003)
  111. Huepe C, Aldana-González M Journal Of Statistical Physics 108 (3-4) 527 (2002)
  112. Mori T, Kai Sh Phys. Rev. Lett. 88 (21) (2002)
  113. Boccaletti S, Kurths J et al Physics Reports 366 (1-2) 1 (2002)
  114. Borisyuk G N, Borisyuk R M et al Uspekhi Fizicheskikh Nauk 172 (10) 1189 (2002)
  115. Mikhailov A S, Calenbuhr V From Cells to Societies Springer Series In Synergetics Chapter 7 (2002) p. 155
  116. Rulkov N F Phys. Rev. E 65 (4) (2002)
  117. Rulkov N F, Afraimovich V S et al Phys. Rev. E 64 (1) (2001)
  118. Ivanitsky A M, Nikolaev A R, Ivanitsky G A International Journal Of Psychophysiology 42 (1) 35 (2001)
  119. Sil’kis I G Neurosci Behav Physiol 31 (6) 573 (2001)
  120. Pazó D, Montejo N, Pérez-Muñuzuri V Phys. Rev. E 63 (6) (2001)
  121. 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
  122. Rulkov N F Phys. Rev. Lett. 86 (1) 183 (2001)
  123. Vadivasova T E, Strelkova G I, Anishchenko V S Phys. Rev. E 63 (3) (2001)
  124. Morelli L G, Zanette D H Phys. Rev. E 63 (3) (2001)
  125. Chernavskii D S Uspekhi Fizicheskikh Nauk 170 (2) 157 (2000)
  126. Sanchez E, Matias M A, Perez-Munuzuri V IEEE Trans. Circuits Syst. I 47 (5) 644 (2000)
  127. 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
  128. Giaquinta A, Argentina M, Velarde M G Journal Of Statistical Physics 101 (1-2) 665 (2000)
  129. Ivanitsky A M, Nikolaev A R, Ivanitsky G A Modern Techniques in Neuroscience Research Chapter 35 (1999) p. 971
  130. SÁNCHEZ E, MATÍAS M A Int. J. Bifurcation Chaos 09 (12) 2335 (1999)
  131. Vanag V K Uspekhi Fizicheskikh Nauk 169 (5) 481 (1999)
  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 et al Physica D: Nonlinear Phenomena 128 (2-4) 224 (1999)
  135. Sil’kis I G, Bogdanova O G Neurosci Behav Physiol 29 (3) 305 (1999)
  136. Hampton A, Zanette D H Phys. Rev. Lett. 83 (11) 2179 (1999)
  137. Rodríguez F B, López V 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
  138. Zanette D H, Mikhailov A S Phys. Rev. E 58 (1) 872 (1998)
  139. Kazantsev V B, Nekorkin I, Velarde M G Radiophys Quantum Electron 41 (12) 1101 (1998)
  140. Bazhenov M, Huerta R et al Physica D: Nonlinear Phenomena 116 (3-4) 392 (1998)
  141. Belykh I V Radiophys Quantum Electron 41 (12) 1066 (1998)
  142. Sil’kis I G, Bogdanova O G Neurosci Behav Physiol 28 (6) 645 (1998)
  143. 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
  144. Nekorkin V I, Makarov V A, Velarde M G Phys. Rev. E 58 (5) 5742 (1998)
  145. Nekorkin V I, Kazantsev V B et al Phys. Rev. E 57 (3) 3344 (1998)
  146. Makarenko V, Llinás R Proc. Natl. Acad. Sci. U.S.A. 95 (26) 15747 (1998)
  147. Sánchez E, Matías M A Phys. Rev. E 57 (5) 6184 (1998)
  148. Battogtokh D, Hildebrand M et al Physics Reports 288 (1-6) 435 (1997)
  149. Rabinovich M I, Abarbanel H D I et al IEEE Trans. Circuits Syst. I 44 (10) 997 (1997)
  150. Zanette D H, Mikhailov A S Physics Letters A 235 (2) 135 (1997)
  151. Zanette D H Phys. Rev. E 55 (5) 5315 (1997)
  152. Vanag V K J. Phys. Chem. A 101 (38) 7074 (1997)
  153. 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
  154. Rabinovich M I Radiophys Quantum Electron 39 (6) 502 (1996)
© 1918–2025 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions