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Synchronization of delay-coupled oscillator networks

 a,  a, b
a 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
b N.I. Lobachevskii Nizhnii Novgorod State University, prosp. Gagarina 23, Nizhnii Novgorod, Russian Federation

Research on synchronization of delay-coupled oscillator networks is reviewed. A number of key research approaches using different models and methods are described and major results obtained through their use are presented and generalized. The most characteristic properties of time-delay coupled systems are discussed.

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Fulltext is also available at DOI: 10.3367/UFNe.0183.201312c.1323
PACS: 05.45.−a, 05.45.Xt, 87.10.−e (all)
DOI: 10.3367/UFNe.0183.201312c.1323
URL: https://ufn.ru/en/articles/2013/12/c/
000332531200003
2-s2.0-84897772184
2013PhyU...56.1217K
Citation: Klinshov V V, Nekorkin V I "Synchronization of delay-coupled oscillator networks" Phys. Usp. 56 1217–1229 (2013)
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Received: 5th, February 2013, revised: 18th, April 2013, 7th, May 2013

Оригинал: Клиньшов В В, Некоркин В И «Синхронизация автоколебательных сетей с запаздывающими связями» УФН 183 1323–1336 (2013); DOI: 10.3367/UFNr.0183.201312c.1323

References (180) ↓ Cited by (40) Similar articles (20)

  1. Huygens Ch Œuvres Complètes (Amsterdam: Swets and Zeitlinger, 1967)
  2. Strutt J W (Baron Rayleigh) The Theory Of Sound (New York: Dover Publ., 1945); Strett Dzh V (lord Relei) Teoriya Zvuka (M.: Gostekhizdat, 1955)
  3. Appleton E V Proc. Cambr. Philos. Soc. 21 231 (1922)
  4. Van der Pol B Philos. Mag. 3 64 (1927)
  5. Andronov A A, Vitt A A Zhurn. Priklad. Fiziki 7 (4) 3 (1930); Andronov A A Sobranie Trudov (Otv. red. M A Leontovich) (M.: Izd-vo AN SSSR, 1956) p. 70
  6. Andronow A, Witt A Arch. Elektrotech. 24 99 (1930); Andronov A A, Vitt A AAndronov A A Sobranie Trudov (Otv. red. M A Leontovich) (M.: Izd-vo AN SSSR, 1956) p. 51
  7. Blekhman I I Sinkhronizatsiya Dinamicheskikh Sistem (M.: Nauka, 1971)
  8. Blekhman I I Sinkhronizatsiya v Prirode i Tekhnike (M.: Nauka, 1981); Blekhman I I Synchronization In Science And Technology (New York: ASME Press, 1988)
  9. Gaponov-Grekhov A V, Rabinovich M I, Starobinets I M Pis’ma ZhETF 39 561 (1984); Gaponov-Grekhov A V, Rabinovich M I, Starobinets I M JETP Lett. 39 688 (1984)
  10. Afraimovich V S, Verichev N N, Rabinovich M I Izv. Vuzov Radiofizika 29 1050 (1986); Afraimovich V S, Verichev N N, Rabinovich M I Radiophys. Quantum Electron. 29 795 (1986)
  11. Siegman A E Lasers (Mill Valley, Callif.: Univ. Science Books, 1986)
  12. Roy R, Thornburg K S (Jr.) Phys. Rev. Lett. 72 2009 (1994)
  13. Lindsey W C Synchronization Systems In Communication And Control (Englewood Cliffs, N.J.: Prentice Hall, 1972); Lindsei V Sistemy Sinkhronizatsii v Svyazi i Upravlenii (M.: Sov. radio, 1978)
  14. Shakhgil’dyan V V, Lyakhovkin A A Fazovaya Avtopodstroika Chastoty (M.: Svyaz’, 1966)
  15. Afraimovich V S i dr. Ustoichivost’, Struktury i Khaos v Nelineinykh Setyakh Sinkhronizatsii (Pod obshch. red. A V Gaponova-Grekhova, M I Rabinovicha) (Gor’kii: IPF AN SSSR, 1989); Afraimovich V S et al. Stability, Structures, And Chaos In Nonlinear Synchronization Networks (Eds A V Gaponov-Grekhov, M I Rabinovich) (Singapore: World Scientific, 1994)
  16. Kuramoto Y Chemical Oscillations, Waves, And Turbulence (Berlin: Springer-Verlag, 1984)
  17. Winfree A T The Geometry Of Biological Time (New York: Springer, 2001)
  18. Glass L, Mackey M C From Clocks To Chaos: The Rhythms Of Life (Princeton, N.J.: Princeton Univ. Press, 1988); Glass L, Meki M Ot Chasov k Khaosu: Ritmy Zhizni (M.: Mir, 1991)
  19. Glass L Nature 410 277 (2001)
  20. Nekorkin V I Usp. Fiz. Nauk 178 313 (2008); Nekorkin V I Phys. Usp. 51 295 (2008)
  21. Borisyuk G N i dr. Usp. Fiz. Nauk 172 1189 (2002); Borisyuk G N et al. Phys. Usp. 45 1073 (2002)
  22. Andronov A A Sobranie Trudov (Otv. red. M A Leontovich) (M.: Izd-vo AN SSSR, 1956)
  23. Krylov N M, Bogolyubov N N Izv. AN SSSR VII ser. Otd. matem. i estestv. nauk (4) 475 (1933)
  24. Bogolyubov N N, Mitropol’skii Yu A Asimptoticheskie Metody v Teorii Nelineinykh Kolebanii (M.: Fizmatgiz, 1958); Bogoliubov N N, Mitropolsky Y A Asymptotic Methods In The Theory Of Non-linear Oscillations (New York: Gordon and Breach Sci. Publ., 1961)
  25. Landa P S Avtokolebaniya v Sistemakh s Konechnym Chislom Stepenei Svobody (M.: Nauka, 1980)
  26. Neimark Yu I, Landa P S Stokhasticheskie i Khaoticheskie Kolebaniya (M.: Nauka, 1988); Neimark Yu I, Landa P S Stochastic And Chaotic Oscillations (Dordrecht: Kluwer Acad. Publ., 1992)
  27. Anishchenko V S i dr. Sinkhronizatsiya Regulyarnykh, Khaoticheskikh i Stokhasticheskikh Kolebanii (M. - Izhevsk: RKhD, 2008)
  28. Pecora L M, Carroll T L Phys. Rev. Lett. 64 821 (1990)
  29. Pecora L M, Carroll T L Phys. Rev. A 44 2374 (1991)
  30. Nekorkin V I, Velarde M G Synergetic Phenomena In Active Lattices: Patterns, Waves, Solitons, Chaos (Berlin: Springer, 2002)
  31. Osipov G V, Kurths J, Zhou Ch Synchronization In Oscillatory Networks (Berlin: Springer, 2007)
  32. Trubetskov D I Sinkhronizatsiya: Uchenyi i Vremya (Saratov: Kolledzh, 2006)
  33. Dmitriev A S, Panas A I Dinamicheskii Khaos: Novye Nositeli Informatsii dlya Sistem Svyazi (M.: Fizmatlit, 2002)
  34. Leonov G A, Smirnova B V Matematicheskie Problemy Teorii Fazovoi Sinkhronizatsii (SPb.: Nauka, 2000)
  35. Belykh V N, Belykh I V, Mosekilde E Phys. Rev. E 63 036216 (2001)
  36. Belykh I, Belykh V, Hasler M Chaos 16 015102 (2006)
  37. Kuznetsov A P, Stankevich N V, Turukina L V Physica D 238 1203 (2009)
  38. Kim S-Y et al. Phys. Rev. E 67 016217 (2003)
  39. Abarbanel’ G D i dr. Usp. Fiz. Nauk 166 363 (1996); Abarbanel H D et al. Phys. Usp. 39 337 (1996)
  40. Rabinovich M I, Myuezinolu M K Usp. Fiz. Nauk 180 371 (2010); Rabinovich M I, Muezzinoglu M K Phys. Usp. 53 357 (2010)
  41. Anishchenko V S, Astakhov S V Usp. Fiz. Nauk 183 1009 (2013); Anishchenko V S, Astakhov S V Phys. Usp. 5 6 (10)
  42. Pikovsky A, Rosenblum M, Kurths J Synchronization: A Universal Concept In Nonlinear Sciences (Cambridge: Cambridge Univ. Press, 2001)
  43. Shil’nikov L P Metody Kachestvennoi Teorii v Nelineinoi Dinamike Vol. 1 (M. - Izhevsk: In-t komp’yut. issled., 2004)
  44. Dmitriev A S, Kislov V Ya Ctokhasticheskie Kolebaniya v Radiofizike i Elektronike (M.: Nauka, 1989)
  45. Kilias T et al. Int. J. Electron. 79 737 (1995)
  46. Leonov G A, Seledzhi S M Vestnik SPbGU Ser. 10. Priklad. matem., informatika, protsessy upravleniya (1) 36 (2004)
  47. Ryskin N M Izv. Vuzov Radiofizika 47 129 (2004); Ryskin N M Radiophys. Quantum Electron. 47 116 (2004)
  48. Leonov G, Seledzhi S Int. J. Bifurcation Chaos 15 1347 (2005)
  49. Leonov G A, Seledzhi S M Avtomat. Telemekh. (3) 11 (2005); Leonov G A, Seledzhi S M Automat. Remote Control 66 348 (2005)
  50. Leonov G, Seledzhi S Int. J. Innovat. Comput. Inform. Control 1 779 (2005)
  51. Arino O, Hbid M L, Ait Dads E (Eds) Delay Differential Equations And Applications (NATO Science Series, Ser. II) Vol. 205 (Dordrecht: Springer, 2006)
  52. Balachandran B, Kalmár-Nagy T, Gilsinn D (Eds) Delay Differential Equations: Recent Advances And New Directions (New York: Springer, 2009)
  53. Ryskin N M, Khavroshin O S Radiotekhnika Elektronika 56 741 (2011); Ryskin N M, Khavroshin O S J. Commun. Technol. Electron. 56 690 (2011)
  54. Usacheva S A, Ryskin N M Physica D 241 372 (2012)
  55. Kozyreff G, Vladimirov A G, Mandel P Phys. Rev. E 64 016613 (2001)
  56. Vladimirov A G, Turaev D V Izv. Vuzov Radiofizika 47 857 (2004); Vladimirov A G, Turaev D V Radiophys. Quantum Electron. 47 769 (2004)
  57. Kim M-Y et al. Phys. Rev. Lett. 94 088101 (2005)
  58. Wünsche H-J et al. Phys. Rev. Lett. 94 163901 (2005)
  59. Vicente R et al. Phys. Rev. E 73 047201 (2006)
  60. Nizette M et al. Physica D 218 95 (2006)
  61. Flunkert V et al. Phys. Rev. E 79 065201(R) (2009)
  62. Zamora-Munt J et al. Phys. Rev. Lett. 105 264101 (2010)
  63. Masoller C et al. Phys. Rev. A 84 023838 (2011)
  64. Rebrova N et al. Phys. Rev. E 83 066202 (2011)
  65. Otto C et al. New J. Phys. 14 113033 (2012)
  66. Kashchenko S A, Grigor’eva E V Relaksatsionnye Kolebaniya v Lazerakh (M.: LIBROKOM, 2013)
  67. Golomb D, Ermentrout G B Network 11 221 (2000)
  68. Takamatsu A, Fujii T, Endo I Phys. Rev. Lett. 85 2026 (2000)
  69. Oprisan S A, Prinz A A, Canavier C C Biophys. J. 87 2283 (2004)
  70. Bazhenov M, Rulkov N F, Timofeev I J. Neurophysiol. 100 1562 (2008)
  71. Friedrich J, Kinzel W J. Comput. Neurosci. 27 65 (2009)
  72. Masoller C, Torrent M C, García-Ojalvo J Philos. Trans. A 367 3255 (2009)
  73. Kashchenko S A, Maiorov V V Modeli Volnovoi Pamyati (M.: URSS, 2009)
  74. Faro J, Velasco S Physica D 110 313 (1997)
  75. Tass P et al. Phys. Rev. E 54 R2224 (1996)
  76. Haken H Eur. Phys. J. B 18 545 (2000)
  77. Trubetskov D I, Mchedlova E S, Krasichkov L V Vvedenie v Teoriyu Samoorganizatsii Otkrytykh Sistem (M.: Fizmatlit, 2005)
  78. Lakshmanan M, Senthilkumar D V Dynamics Of Nonlinear Time-Delay Systems (Berlin: Springer, 2010)
  79. Gray C M et al. Nature 338 334 (1989)
  80. Engel A K et al. Science 252 1177 (1991)
  81. Frien A et al. NeuroReport 5 2273 (1994)
  82. Singer W, Gray C M Annu. Rev. Neurosci. 18 555 (1995)
  83. Courtemanche R, Lamarre Y J. Neurophysiol. 93 2039 (2005)
  84. Schoffelen J-M, Oostenveld R, Fries P Science 308 111 (2005)
  85. Doesburg S M, Ward L M Int. Congress Ser. 1300 551 (2007)
  86. Uhlhaas P J et al. Front. Integr. Neurosci. 3 17 (2009)
  87. Wu J (Ed.) Handbook On Theoretical And Algorithmic Aspects Of Sensor, Ad Hoc Wireless, And Peer-to-Peer Networks (New York: Auerbach Publ., 2005)
  88. Akyildiz I F et al. Comput. Networks 38 393 (2002)
  89. Sundararaman B, Buy U, Kshemkalyani A D Ad Hoc Networks 3 281 (2005)
  90. Demirkol I, Ersoy C, Alagoz F IEEE Commun. Mag. 44 115 (2006)
  91. Larger L et al. Opt. Express 20 3241 (2012)
  92. Brunner D et al. Nature Commun. 4 1364 (2013)
  93. Bellman R, Cooke K L Differential-Difference Equations (New York: Academic Press, 1963); Bellman R, Kuk K L Differentsial’no-raznostnye Uravneniya (M: Mir, 1967)
  94. Leonov G A, Ponomarenko D V, Smirnova V B Frequency-Domain Methods For Nonlinear Analysis. Theory And Applications (Singapore: World Scientific, 1996)
  95. Leonov G A, Smirnova V B Math. Nachr. 177 157 (1996)
  96. Kaschenko D, Kaschenko S, Schwarz W Int. J. Bifurcation Chaos 22 1250184 (2012)
  97. Daan S, Berde C J. Theor. Biol. 70 297 (1978)
  98. Neu J C SIAM J. Appl. Math. 37 307 (1979)
  99. Ermentrout G B J. Math. Biol. 12 327 (1981)
  100. Hoppensteadt F C, Keener J P J. Math. Biol. 15 339 (1982)
  101. Kopell N, Ermentrout G B Commun. Pure Appl. Math. 39 623 (1986)
  102. Acebroń J A et al. Rev. Mod. Phys. 77 137 (2005)
  103. Izhikevich E M Phys. Rev. E 58 905 (1998)
  104. Schuster H G, Wagner P Prog. Theor. Phys. 81 939 (1989)
  105. Yeung M K S, Strogatz S H Phys. Rev. Lett. 82 648 (1999)
  106. Earl M G, Strogatz S H Phys. Rev. E 67 036204 (2003)
  107. Dorizzi B, Grammaticos B Phys. Rev. A 44 6958 (1991)
  108. Niebur E, Schuster H G, Kammen D M Phys. Rev. Lett. 67 2753 (1991)
  109. Nakamura Y, Tominaga F, Munakata T Phys. Rev. E 49 4849 (1994)
  110. D’Huys O et al. Chaos 18 037116 (2008)
  111. Zanette D H Phys. Rev. E 62 3167 (2000)
  112. Ko T-W, Ermentrout G B Phys. Rev. E 76 056206 (2007)
  113. Jeong S-O, Ko T-W, Moon H-T Phys. Rev. Lett. 89 154104 (2002)
  114. Campbell S A, Kobelevskiy I Discrete Continuous Dyn. Syst. 32 2653 (2012)
  115. Aronson D G, Ermentrout G B, Kopell N Physica D 41 403 (1990)
  116. Ramana Reddy D V, Sen A, Johnston G L Physica D 129 15 (1999)
  117. Klin’shov V V, Kazantsev V B, Nekorkin V I Izv. Vuzov Prikladnaya nelineinaya dinamika 12 (6) 129 (2004)
  118. Ramana Reddy D V, Sen A, Johnston G L Phys. Rev. Lett. 80 5109 (1998)
  119. Ramana Reddy D V, Sen A, Johnston G L Phys. Rev. E 69 056217 (2004)
  120. Strogatz S H Nature 394 316 (1998)
  121. Mirollo R E, Strogatz S H J. Stat. Phys. 60 245 (1990)
  122. Ramana Reddy D V, Sen A, Johnston G L Phys. Rev. Lett. 85 3381 (2000)
  123. D’Huys O et al. Chaos 20 043127 (2010)
  124. Wirkus S, Rand R Nonlin. Dynamics 30 205 (2002)
  125. Song Y, Xu J, Zhang T Chaos 21 023111 (2011)
  126. Choe C-U et al. Phys. Rev. E 75 046206 (2007)
  127. Choe C-U et al. Phys. Rev. E 81 025205(R) (2010)
  128. Zou W et al. Phys. Rev. E 84 066208 (2011)
  129. Selivanov A A et al. Phys. Rev. E 85 016201 (2012)
  130. Mirollo R E, Strogatz S H SIAM J. Appl. Math. 50 1645 (1990)
  131. Ermentrout G B, Kopell N J. Math. Biol. 29 195 (1991)
  132. Kuramoto Y Physica D 50 15 (1991)
  133. Bottani S Phys. Rev. Lett. 74 4189 (1995)
  134. Canavier C C, Achuthan S Math. Biosci. 226 77 (2010)
  135. Peskin C S Mathematical Aspects Of Heart Physiology (New York: Courant Institute of Mathematical Sciences, New York Univ., 1975)
  136. Izhikevich E M IEEE Trans. Neural Networks 10 508 (1999)
  137. Glass L Nature 410 277 (2001)
  138. Glass L et al. Phys. Rev. E 65 021908 (2002)
  139. Goel P, Ermentrout B Physica D 163 191 (2002)
  140. Loskutov A, Rybalko S, Zhuchkova E Int. J. Bifurcation Chaos 14 2457 (2004)
  141. Rybalko S, Zhuchkova E Int. J. Bifurcation Chaos 19 263 (2009)
  142. Klinshov V V, Nekorkin V I Commun. Nonlinear Sci. Numer. Simulat. 18 973 (2013)
  143. Neimark Yu I Metod Tochechnykh Otobrazhenii v Teorii Nelineinykh Kolebanii (M.: Nauka, 1972)
  144. Ernst U, Pawelzik K, Geisel T Phys. Rev. Lett. 74 1570 (1995)
  145. Ernst U, Pawelzik K, Geisel T Phys. Rev. E 57 2150 (1998)
  146. Zeitler M, Daffertshofer A, Gielen C C A M Phys. Rev. E 79 065203(R) (2009)
  147. Coombes S, Lord G J Phys. Rev. E 55 R2104 (1997)
  148. Coombes S, Lord G J Phys. Rev. E 56 5809 (1997)
  149. Klinshov V V, Nekorkin V I Chaos Solitons Fractals 44 98 (2011)
  150. Prasad A et al. Phys. Rev. E 74 035204(R) (2006)
  151. Prasad A et al. Chaos 18 023111 (2008)
  152. Adhikari B M, Prasad A, Dhamala M Chaos 21 023116 (2011)
  153. Klinshov V, Nekorkin V Cybernetics Phys. 1 106 (2012)
  154. Ermentrout G B, Kopell N Proc. Natl. Acad. Sci. USA 95 1259 (1998)
  155. Neves F S, Timme M J. Phys. A Math. Theor. 42 345103 (2009)
  156. Gerstner W Phys. Rev. Lett. 76 1755 (1996)
  157. Klinshov V V, Nekorkin V I Discontinuity Nonlinearity Complexity 1 253 (2012)
  158. Wu W, Chen T Nonlinearity 20 789 (2007)
  159. Wu W, Chen T Int. J. Neural Syst. 19 425 (2009)
  160. Wu W, Liu B, Chen T Neural Networks 23 783 (2010)
  161. Wang S et al. PLoS Comput. Biol. 8 e1002306 (2012)
  162. Timme M, Wolf F, Geisel T Phys. Rev. Lett. 89 258701 (2002)
  163. Foss J, Milton J J. Neurophysiol. 84 975 (2000)
  164. Woodman M, Canavier C Front. Syst. Neurosci. Conf. Abstract. Computational And Systems Neuroscience (2009)
  165. Woodman M M, Canavier C C J. Comput. Neurosci. 31 401 (2011)
  166. Campbell S R, Wang D Physica D 111 151 (1998)
  167. Rossoni E et al. Phys. Rev. E 71 061904 (2005)
  168. Burič N, Todorovič D Phys. Rev. E 68 066218 (2003)
  169. Oguchi T, Nijmeijer H, Yamamoto T Chaos 18 037108 (2008)
  170. Michiels W, Nijmeijer H Chaos 19 033110 (2009)
  171. Jüngling T et al. Phys. Rev. E 84 056208 (2011)
  172. Manju Shrii M, Senthilkumar D V, Kurths J Europhys. Lett. 98 10003 (2012)
  173. Burič N, Todorovič D Phys. Rev. E 67 066222 (2003)
  174. Huber D, Tsimring L S Phys. Rev. Lett. 91 260601 (2003)
  175. Jiang Y Phys. Lett. A 267 342 (2000)
  176. Masoller C, de S Cavalcante H L D, Rios Leite J R Phys. Rev. E 64 037202 (2001)
  177. Masoller C, Marti A C Phys. Rev. Lett. 94 134102 (2005)
  178. Wang Q et al. Phys. Rev. E 80 026206 (2009)
  179. Masoller C, Atay F M Eur. Phys. J. D 62 119 (2011)
  180. Koronovskii A A, Moskalenko O I, Khramov A E Usp. Fiz. Nauk 179 1281 (2009); Koronovskii A A, Moskalenko O I, Hramov A E Phys. Usp. 52 1213 (2009)

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