ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


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Kryukov A. K., Osipov G. V., Polovinkin A. V. Variety of synchronous regimes in ensembles of nonidentical oscillators: Chain and lattice. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 2, pp. 29-36. DOI: 10.18500/0869-6632-2009-17-2-29-36

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Language: 
Russian
Article type: 
Article
UDC: 
621.391.01

Variety of synchronous regimes in ensembles of nonidentical oscillators: Chain and lattice

Autors: 
Kryukov Aleksej Konstantinovich, Lobachevsky State University of Nizhny Novgorod
Osipov Grigorij Vladimirovich, Lobachevsky State University of Nizhny Novgorod
Polovinkin Andrej Vladimirovich, Lobachevsky State University of Nizhny Novgorod
Abstract: 

We study synchronization in one- and two-dimentional ensembles of nonidentical Bonhoeffer–van der Pol oscillators. Small chains (number of elements N <= 4) are proved to have not less than 2 N−1 coexisting stable different synchronous regimes. The chain of N elements is supposed to have not less than 2 N−1 synchronous regimes at the same values of parameters. Formation of synchronization clusters at weak coupling is shown. Regimes, provided by existing of waves, setting rhythm for all elements in ensemble, are investigated.

Reference: 
  1. Maurer J, Libchaber A. Effect of the Prandtl number on the onset of turbulence in liquid. J.Phys. Lett. (France) 1982;41(21):515–518.
  2. Brun E, Derighette B, Meier D, Holzner R, Raveni M. Observation of order and chaos in a nuclear-spin ip laser. J.Opt.Soc.Am. B. 1985;2:156–167.
  3. Dangoisse D, Glorieux P, Hennequin D. Chaos in a CO2 laser with modulated parameters. Phys. Rev. A. 1987;36(10):4775–4791. DOI: 10.1103/PhysRevA.36.4775.
  4. Thompson JMT, Stewart HB. Nonlinear Dynamics and Chaos. Wiley, Chichester, 1986. 376 p.
  5. Foss J, Longtin A, Mensour B, Milton J. Multistability and delayed recurrent loops. Phys Rev Lett. 1996;76(4):708-711. DOI: 10.1103/PhysRevLett.76.708.
  6. Simonotto E, Riani M, Seife C, Roberts M, Twitty J, Moss F. Visual Perception of Stochastic Resonance. Phys. Rev. Lett. 1997;78:1186–1189. DOI: 10.1103/PHYSREVLETT.78.1186.
  7. Pikovsky AS, Rosenblum MG, Kurths J. Synchronization. A Universal Concept in Nonlinear Sciences. Cambridge: Cambridge University Press; 2001. 433 p. DOI: 10.1017/CBO9780511755743.
  8. Mosekilde E, Maistrenko Yu, Postnov D. Chaotic Synchronization: Applications to Living Systems. Singapore: World Scientific; 2002. 440 p. DOI: 10.1142/4845.
  9. Osipov GV, Kurths J, Zhou Ch. Synchronization in Oscillatory Networks. Berlin: Springer; 2007. 372 p.
  10. Sompolinsky H, Kanter I. Temporal association in asymmetric neural networks Phys. Rev. Lett. 1986;57:2861–2864. DOI: 10.1103/PhysRevLett.57.2861.
  11. Canavier CC, Baxter DA, Clark JW, Byrne JH. Nonlinear dynamics in a model neuron provide a novel mechanism for transient synaptic inputs to produce long-term alterations of postsynaptic activity. J Neurophysiol. 1993;69(6):2252-2257. DOI: 10.1152/jn.1993.69.6.2252.
  12. Rabinovich MI, Varona P, Selverston AI, Abarbanel HDI. Dynamical principles in neuroscience. Rev. of Modern Phys. 2006;78:1213–1265. DOI: 10.1103/REVMODPHYS.78.1213.
  13. Bonhoeffer KF. Modelle der Nervenerregung. Naturwissenschaften. 1953;40:301–311.
  14. Torre V. A theory of synchronization of heart pace-maker cells. J.Theor.Biol. 1976;61:55–71.
  15. Osipov GV, Sushchik MM. Synchronized clusters and multistability in arrays of oscillators with different natural frequencies. Phys.Rev.E. 1998;58(6):7198. DOI: 10.1103/PhysRevE.58.7198.
  16. Macleod K, Backer A, Laurent G. Who reads temporal information contained across synchronized and oscillatory spike trains? Nature. 1998;395:693–698.
  17. Ambiguity in Mind and Nature. Eds P. Kruse and M. Stadler. New York: Springer-Verlag. 1995. 327 p.
  18. Mensour B, Longtin A. Controlling chaos to store information in delay-differential equations. Phys. Lett. A. 1995:205(1):18–24.
  19. Beuter A, Milton JG, Labrie C, Glass L. Complex motor dynamics and control in multi-loop negative feedback systems. IEEE Systems Man Cybern. 1989;3:899–902. DOI: 10.1109/ICSMC.1989.71426.
Received: 
15.08.2008
Accepted: 
01.12.2008
Published: 
30.06.2009
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