Issues

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1996

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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)
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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 (148) ↓ Similar articles (20)

  1. Herault J, Paez L et al Phys. Rev. E 110 (5) (2024)
  2. Di Palo E, Olm J M et al IEEE Trans. Control Netw. Syst. 11 1251 (2024)
  3. Remi T, Subha P A J. Phys. A: Math. Theor. 56 345701 (2023)
  4. Bashkirtseva I A, Pisarchik A N, Ryashko L B Mathematics 11 597 (2023)
  5. Kashchenko S, Mayorov V, Mayorova N Eur. Phys. J. Spec. Top. 232 509 (2023)
  6. Kongni S J, Nguefoue V et al Phys. Rev. E 108 (3) (2023)
  7. Wang Ya, Zhang X, Liang S Nonlinear Dyn 111 19447 (2023)
  8. Luo Z, Bo Y et al 131 (5) (2022)
  9. Glyzin S D, Kolesov A Yu Diff Equat 58 853 (2022)
  10. Belykh I V, Daley K M, Belykh V N Radiophys Quantum El 64 700 (2022)
  11. 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
  12. Chen G IEEE/CAA J. Autom. Sinica 9 573 (2022)
  13. Braga M H Materials 14 2398 (2021)
  14. Iqbal M Results In Control And Optimization 3 100016 (2021)
  15. Sosa R I, Zanette D H Int. J. Bifurcation Chaos 31 2150056 (2021)
  16. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 1 (2021) p. 1
  17. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 6 (2021) p. 211
  18. Cejnar P, Vyšata Oldřich et al Sci Rep 10 (1) (2020)
  19. Mazurov M E Bull. Russ. Acad. Sci. Phys. 84 346 (2020)
  20. Strelkova G I, Anishchenko V S Uspekhi Fizicheskikh Nauk 190 160 (2020) [Strelkova G I, Anishchenko V S Phys.-Usp. 63 145 (2020)]
  21. 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
  22. Budzinski R C, Boaretto B R R et al Communications In Nonlinear Science And Numerical Simulation 75 140 (2019)
  23. Kulminskiy D D, Ponomarenko V I et al Nonlinear Dyn 98 735 (2019)
  24. Khobotov A G, Khil’ko A I, Tel’nykh A A Radiophys Quantum El 61 69 (2018)
  25. Murray J D, Demirtaş M, Anticevic A Biological Psychiatry: Cognitive Neuroscience And Neuroimaging 3 777 (2018)
  26. Glyzin S D Aut. Control Comp. Sci. 52 762 (2018)
  27. Contreras‐Hernández E, Chávez D et al The Journal Of Physiology 596 1747 (2018)
  28. Conde-Saavedra G, Ramírez-Ávila G M 28 (4) (2018)
  29. Ivanitskii G R Phys.-Usp. 61 871 (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. Iqbal M, Rehan M et al PLoS ONE 12 e0176986 (2017)
  32. 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
  33. 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
  34. Bozhokin S V, Zharko S V et al Tech. Phys. 62 837 (2017)
  35. Liu X, Zhang K, Xie W-Ch IEEE Trans. Neural Netw. Learning Syst. 28 1055 (2017)
  36. Makarov V A, Calvo C et al IFAC-PapersOnLine 49 80 (2016)
  37. Guo D, Fu Y Q, Zheng B ChemPhysChem 17 2355 (2016)
  38. Korkmaz N, Öztürk İ, Kılıç R Nonlinear Dyn 86 1841 (2016)
  39. Masulli P, Villa A E P SpringerPlus 5 (1) (2016)
  40. Wright T, Twaddle Ja et al Mathematical Biosciences 273 57 (2016)
  41. Selskii A, Makarov V A Regul. Chaot. Dyn. 21 97 (2016)
  42. Prokin I S, Kazantsev V B Radiophys Quantum El 57 745 (2015)
  43. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 1 (2015) p. 1
  44. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 5 (2015) p. 177
  45. Acedo L, Lamprianidou E et al Physica A: Statistical Mechanics And Its Applications 435 111 (2015)
  46. Cascallares G, Sánchez A D et al Physica A: Statistical Mechanics And Its Applications 433 356 (2015)
  47. Kozma R, Wang Ju, Zeng Zh Springer Handbook of Computational Intelligence Chapter 33 (2015) p. 607
  48. Prado T de L, Lopes S R et al Phys. Rev. E 90 (3) (2014)
  49. Mesbah S, Moghtadaei M et al Chaos, Solitons & Fractals 65 20 (2014)
  50. Ivanitskii G R, Deev A A, Khizhnyak E P Uspekhi Fizicheskikh Nauk 184 43 (2014) [Ivanitskii G R, Deev A A, Khizhnyak E P Phys.-Usp. 57 37 (2014)]
  51. Mitra Ch, Ambika G, Banerjee S Chaos, Solitons & Fractals 69 188 (2014)
  52. Sedov A S, Medvednik R S, Raeva S N Hum Physiol 40 1 (2014)
  53. Heo M, Park J-K, Kim K Procedia Computer Science 29 2515 (2014)
  54. Bozhokin S V, Suslova I M Tech. Phys. 58 1730 (2013)
  55. Wang Q, Zhang H, Chen G Eur. Phys. J. B 86 (7) (2013)
  56. Klinshov V V, Nekorkin V I Phys.-Usp. 56 1217 (2013)
  57. Khobotov A G, I Kh A, I R V Radiophys Quantum El 56 95 (2013)
  58. Hu H, Pang L et al IJIS 03 145 (2013)
  59. Pavlov A N, Hramov A E et al Uspekhi Fizicheskikh Nauk 182 905 (2012)
  60. 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
  61. Rubchinsky L L, Park Ch, Worth R M Nonlinear Dyn 68 329 (2012)
  62. McCULLEN N J, IVANCHENKO M V et al Int. J. Bifurcation Chaos 21 2467 (2011)
  63. Ovchinnikov A A, Hramov A E et al Tech. Phys. 56 1 (2011)
  64. Wang Q, Chen G et al PLoS ONE 6 e15851 (2011)
  65. Ibarz B, Casado J M, Sanjuán M A F Physics Reports 501 1 (2011)
  66. Wang Q, Shi X, Chen G 16 607 (2011)
  67. Sedov A S, Medvednik R S, Raeva S N Neurosci Behav Physi 41 998 (2011)
  68. Hu H, Shi Zh 2011 Seventh International Conference on Natural Computation, (2011) p. 475
  69. Dmitriev A S, Ryzhov A I J. Commun. Technol. Electron. 55 429 (2010)
  70. Kazanovich Ya B, Kazanovich Y B Math.Biol.Bioinf. 5 43 (2010)
  71. Cao H, Ibarz B Phil. Trans. R. Soc. A. 368 5071 (2010)
  72. Wang Q, Perc M et al Physica A: Statistical Mechanics And Its Applications 389 3299 (2010)
  73. Koronovskii A A, Ovchinnikov A A, Hramov A E Phys. Wave Phen. 18 262 (2010)
  74. Li Ya-L, Li R 2010 Second WRI Global Congress on Intelligent Systems, (2010) p. 176
  75. Ivanitskii G R Uspekhi Fizicheskikh Nauk 180 337 (2010)
  76. Yang L, Jia Ya, Yi M 2010 Sixth International Conference on Natural Computation, (2010) p. 819
  77. Rabinovich M I, Muezzinoglu M K Uspekhi Fizicheskikh Nauk 180 371 (2010)
  78. Ivanitsky G R, Deev A A BIOPHYSICS 54 381 (2009)
  79. Wang Q, Perc M et al Phys. Rev. E 80 (2) (2009)
  80. Yan-Long L, Jun M et al Chinese Phys. B 18 4598 (2009)
  81. Koronovskii A A, Moskalenko O I, Hramov A E Uspekhi Fizicheskikh Nauk 179 1281 (2009)
  82. Skonzhenko L A, Krasichkov L V Tech. Phys. Lett. 35 5 (2009)
  83. LI YAN-LONG, MA JUN et al Int. J. Mod. Phys. C 20 1521 (2009)
  84. Li Ya-L, Ma Ju et al Chaos, Solitons & Fractals 37 1083 (2008)
  85. Nekorkin V I Uspekhi Fizicheskikh Nauk 178 313 (2008)
  86. Chik D, Chick D Math.Biol.Bioinf. 3 16 (2008)
  87. Wang Q, Duan Zh et al Europhys. Lett. 83 50008 (2008)
  88. Ibarz B, Casado J M, Sanjuán M A F Phys. Rev. E 75 (4) (2007)
  89. Cubero D, Casado-Pascual Je et al Phys. Rev. E 75 (6) (2007)
  90. Han XiuPing, Lu JunAn SCI CHINA SER F 50 615 (2007)
  91. Skonzhenko L A, Krasichkov L V Tech. Phys. Lett. 33 483 (2007)
  92. Deng X, Geng H, Matache M T Biosystems 88 16 (2007)
  93. Casado J M, Gómez O J, Morillo M Phys. Rev. E 73 (1) (2006)
  94. KUZNETSOV A S, FORTI G L, SHALFEEV V D Int. J. Bifurcation Chaos 16 741 (2006)
  95. Anishchenko V S, Astakhov V et al Nonlinear Dynamics of Chaotic and Stochastic Systems Springer Series In Synergetics Chapter 1 (2006) p. 1
  96. MATACHE MIHAELA T Int. J. Mod. Phys. B 20 897 (2006)
  97. WANG SHENG-JUN, XU XIN-JIAN et al Int. J. Mod. Phys. C 16 1841 (2005)
  98. Volkov E I Radiophys Quantum Electron 48 212 (2005)
  99. Ivanchenko M V, Osipov G V, Shalfeev V D Radiophys Quantum Electron 48 934 (2005)
  100. Ivanchenko M V, Osipov G V et al Phys. Rev. Lett. 93 (13) (2004)
  101. Dodla R R V, Sen A, Johnston G L Communications In Nonlinear Science And Numerical Simulation 8 493 (2003)
  102. Aldana M, Coppersmith S, Kadanoff L P Perspectives and Problems in Nolinear Science Chapter 2 (2003) p. 23
  103. Casado J M, Baltanás J P Phys. Rev. E 68 (6) (2003)
  104. SHILNIKOV ANDREY L, RULKOV NIKOLAI F Int. J. Bifurcation Chaos 13 3325 (2003)
  105. Andreev K V, Krasichkov L V Tech. Phys. Lett. 29 105 (2003)
  106. Casado J M Physics Letters A 310 400 (2003)
  107. ZANETTE DAMIÁN H, MORELLI LUIS G Int. J. Bifurcation Chaos 13 781 (2003)
  108. Boccaletti S, Kurths J et al Physics Reports 366 1 (2002)
  109. Borisyuk G N, Borisyuk R M et al Uspekhi Fizicheskikh Nauk 172 1189 (2002)
  110. Rulkov N F Phys. Rev. E 65 (4) (2002)
  111. Mori T, Kai Sh Phys. Rev. Lett. 88 (21) (2002)
  112. Mikhailov A S, Calenbuhr V From Cells to Societies Springer Series In Synergetics Chapter 7 (2002) p. 155
  113. Pazó D, Montejo N, Pérez-Muñuzuri V Phys. Rev. E 63 (6) (2001)
  114. Rulkov N F, Afraimovich V S et al Phys. Rev. E 64 (1) (2001)
  115. Ivanitsky A M, Nikolaev A R, Ivanitsky G A International Journal Of Psychophysiology 42 35 (2001)
  116. 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
  117. Morelli L G, Zanette D H Phys. Rev. E 63 (3) (2001)
  118. Rulkov N F Phys. Rev. Lett. 86 183 (2001)
  119. Vadivasova T E, Strelkova G I, Anishchenko V S Phys. Rev. E 63 (3) (2001)
  120. Chernavskii D S Uspekhi Fizicheskikh Nauk 170 157 (2000)
  121. 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
  122. Sanchez E, Matias M A, Perez-Munuzuri V IEEE Trans. Circuits Syst. I 47 644 (2000)
  123. Hampton A, Zanette D H Phys. Rev. Lett. 83 2179 (1999)
  124. Mariño I P, Pérez-Muñuzuri V et al Physica D: Nonlinear Phenomena 128 224 (1999)
  125. 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
  126. Zanette D H Europhys. Lett. 45 424 (1999)
  127. KOZLOV A K, SUSHCHIK M M et al Int. J. Bifurcation Chaos 09 2271 (1999)
  128. Sil’kis I G, Bogdanova O G Neurosci Behav Physiol 29 305 (1999)
  129. Ivanitsky A M, Nikolaev A R, Ivanitsky G A Modern Techniques in Neuroscience Research Chapter 35 (1999) p. 971
  130. Vanag V K Uspekhi Fizicheskikh Nauk 169 481 (1999)
  131. SÁNCHEZ E, MATÍAS M A Int. J. Bifurcation Chaos 09 2335 (1999)
  132. 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
  133. Kazantsev V B, Nekorkin I, Velarde M G Radiophys Quantum Electron 41 1101 (1998)
  134. Bazhenov M, Huerta R et al Physica D: Nonlinear Phenomena 116 392 (1998)
  135. Sánchez E, Matías M A Phys. Rev. E 57 6184 (1998)
  136. Zanette D H, Mikhailov A S Phys. Rev. E 58 872 (1998)
  137. Nekorkin V I, Kazantsev V B et al Phys. Rev. E 57 3344 (1998)
  138. Makarenko V, Llinás R Proc. Natl. Acad. Sci. U.S.A. 95 15747 (1998)
  139. Nekorkin V I, Makarov V A, Velarde M G Phys. Rev. E 58 5742 (1998)
  140. Belykh I V Radiophys Quantum Electron 41 1066 (1998)
  141. Sil’kis I G, Bogdanova O G Neurosci Behav Physiol 28 645 (1998)
  142. Zanette D H Phys. Rev. E 55 5315 (1997)
  143. Vanag V K J. Phys. Chem. A 101 7074 (1997)
  144. Battogtokh D, Hildebrand M et al Physics Reports 288 435 (1997)
  145. Zanette D H, Mikhailov A S Physics Letters A 235 135 (1997)
  146. Rabinovich M I, Abarbanel H D I et al IEEE Trans. Circuits Syst. I 44 997 (1997)
  147. Rabinovich M I Radiophys Quantum Electron 39 502 (1996)
  148. 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

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