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

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Neiman A. B., Russell D., Moss F., Schimansky-Geier L. . Synchronization, noise and electroreceptors. Izvestiya VUZ. Applied Nonlinear Dynamics, 2003, vol. 11, iss. 3, pp. 84-94. DOI: 10.18500/0869-6632-2003-11-3-84-94

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English
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
537.86:519.2: 577.359
DOI: 
10.18500/0869-6632-2003-11-3-84-94

Synchronization, noise and electroreceptors

Autors: 
Neiman Aleksander Borisovich, Ohio University
Russell David, University of Missouri-St. Louis
Moss Frank, University of Missouri-St. Louis
Schimansky-Geier Lutz , University of Portsmouth
Abstract: 

Classical notion of synchronization, introduced originally for periodical self-sustained oscillators, can be extended to stochastic systems. This can be done even in the case when the characteristic times of a system are fully controlled by noise. Stochastic synchronization is then defined by imposing certain conditions to various statistical measures of the process. We teview various approaches to stochastic synchronization and apply them to study synchronization in the electrosensory system of paddlefish.

Key words: 
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Acknowledgments: 
This work was supported by the Office of Naval Research - Physics Division, the National Institutes of Health (ROIDC004922-01), the National Science Foundation (INT-0128974) and DAAD (D/0104610). A.N., F.M. and L.S.-G. thank Prof. Vadim Anishchenko for numerious stimulating discussions оn topics of stochastic sychronization.
Reference: 
  1. Blekhman I. Synchronization in Science and Technology. New York: ASME Press; 1988. 350 p.
  2. Glass L, Mackey MC. From Clocks to Chaos. The Rythms of Life. Princeton, NJ: Princeton University Press; 1988. 272 p.
  3. Soen Y, Cohen N, Lipson D, Braun E. Emergence of spontaneous rhythm disorders in self-assembled networks оf heart cells. Phys. Rev. Lett. 1999;82(17):3556–3559. DOI: 10.1103/PhysRevLett.82.3556.
  4. Elson RC, Selverston HR, Rulkov NF, Rabinovich MI, Abarbanel HDI. Synchronous behavior of two coupled biological neurons. Phys. Rev. Lett. 1998;81(25):5692–5695. DOI: 10.1103/PhysRevLett.81.5692.
  5. Neiman А, Pei X, Russell DF, Wojtenek W, Wilkens L, Moss F, Braun HA, Huber MT, Voigr K. Synchronization оf the electrosensitive cells in the paddlefish. Phys. Rev. Lett. 1999;82(3):660–663. DOI: 10.1103/PhysRevLett.82.660.
  6. Bahar S, Neiman A, Wilkens L, Moss F. Synchronization and stochastic resonance effects in the crayfish caudal photoreceptor. Phys. Rev. Е. 2002;65(5):050901. DOI: 10.1103/PhysRevE.65.050901.
  7. Tass Р, Rosenblum M, Weule J, Kurths J, Pikovsky А, Volkmann J, Schnitzler A, Freund H. Detection of n:m phase locking from noisy data: Application to magnetoencephalography. Phys. Rev. Lett. 1998;81(15):3291–3294. DOI: 10.1103/PhysRevLett.81.3291.
  8. Schifer C, Rosenblum MG, Abel H, Kurths J. Synchronization in the human cardiorespiratory system. Phys. Rev. Е. 1999;60(1):857–870. DOI: 10.1103/PhysRevE.60.857.
  9. Anishchenko VS, Balanov AG, Janson NB, Igosheva NB, Bordukov GV. Entrainment between heart rate and weak noninvasive forcing. Int. J. Bifurc. Chaos. 2000;10(10):2339–2348. DOI: 10.1142/S0218127400001468.
  10. Winfree AT. The Geometry of Biological Time. New York: Springer; 1980. 530 p. DOI: 10.1007/978-3-662-22492-2.
  11. Pikovsky AS, Rosenblum MG, Kurths J. Synchronization. A Universal Concept in Nonlinear Sciences. Cambridge: Cambridge University Press; 2001. 411 p. DOI: 10.1017/CBO9780511755743.
  12. Andronov А, Witt А, Khaykin S. Theory оf Oscillations. Oxford: Pergamon Press; 1966.
  13. Pecora LM, Carroll TL. Synchronization in chaotic systems. Phys. Rev. Lett. 1990;64(8):821–824. DOI: 10.1103/PhysRevLett.64.821.
  14. Anishchenko VS, Vadivasova TE, Postnov DE, Safonova MA. Forced and mutual chaos synchronization. J. Commun. Technol. Electron. 1991;36(2):338–351 (in Russian).
  15. Anishchenko VS, Vadivasova TE, Postnov DE, Safonova MA. Synchronization оf chaos. Int. J. Bifurc. Chaos. 1992;2(3):633–644. DOI: 10.1142/S0218127492000756.
  16. Rosenblum MG, Pikovsky AS, Kurths J. Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 1996;76(11):1804–1807. DOI: 10.1103/PhysRevLett.76.1804.
  17. Stratonovich RL. Topics in the Theory of Random Noise. New York: Gordon and Breach; 1981.
  18. Neiman А, Silchenko А, Anishchenko V, Schimansky-Geier L. Stochastic resonance: noise-enhanced phase coherence. Phys. Rev. Е. 1998;58(6):7118–7125. DOI: 10.1103/PhysRevE.58.7118.
  19. Malakhov AN. Fluctuations in Auto-Oscillation Systems. Moscow: Nauka; 1968 (in Russian).
  20. Anishchenko VS, Astakhov VV, Neiman AB, Vadivasova TE, Schimansky-Geier L. Nonlinear Dynamics of Chaotic and Stochastic Systems. Berlin: Springer; 2002. 446 p.
  21. Bendat JS, Piersol AG. Random Data. John Wiley and Sons; 1986. 640 p.
  22. Callenbach L, Hinggi Р, Linz SJ, Freund JA, Schimansky-Geier L. Oscillatory systems driven by noise: Frequency and phase synchronization. Phys. Rev. E. 2002;65(5):051110. DOI: 10.1103/PhysRevE.65.051110.
  23. Shulgin B, Neiman А, Anishchenko V. Mean switching frequency locking in stochastic bistable systems driven by а periodic force. Phys. Rev. Lett. 1995;75(23):4157–4160. DOI: 10.1103/PhysRevLett.75.4157.
  24. Neiman A. Synchronizationlike phenomena in coupled stochastic bistable systems. Phys. Rev. Е. 1994;49(4):3484–3488. DOI: 10.1103/PhysRevE.49.3484.
  25. Freund J, Neiman A, Schimansky-Geier L. Analytic description of noise-induced synchronization. Europhysics Letters. 2000;50(1):8–14. DOI: 10.1209/epl/i2000-00228-6.
  26. Wilkens LA, Russell DF, Pei X, Gurgens C. The paddlefish rostrum functions аs аn electrosensory antenna in plankton feeding. Proc. Royal Soc. London В. 1997;264(1389):1723–1729. DOI: 10.1098/rspb.1997.0239.
  27. Neiman А, Russell DF. Stochastic biperiodic oscillations in the electroreceptors оf paddlefish. Phys. Rev. Lett. 2001;86(15):3443–3446. DOI: 10.1103/PhysRevLett.86.3443.
  28. Neiman А, Russell DF. Synchronization оf noise-induced bursts in noncoupled sensory neurons. Phys. Rev. Lett. 2002;88(13):138103. DOI: 10.1103/PhysRevLett.88.138103.
  29. Ermentrout GB, Kореll N. Parabolic bursting in ап excitable system coupled with а slow oscillation. SIAM J. Appl. Math. 1986;46(2):233–253. DOI: 10.1137/0146017.
  30. Izhikevich EM. Neuronal excitability, spiking and bursting. Int. J. Bifurc. Chaos. 2000;10(6):1171–1266. DOI: 10.1142/S0218127400000840.
  31. Naundorf B, Freund JA. Signal detection by means of phase coherence induced through phase resetting. Phys. Rev. Е. 2002;66(4):040901. DOI: 10.1103/PhysRevE.66.040901.
  32. Freund J, Schimansky-Geier L, Beisner B, Neiman А, Russell D, Yakusheva T, Moss F. Behavioral stochastic resonance: How the noise from a daphnia swarm enhances individual prey Capture by juvenile paddlefish. Journal of Theoretical Biology. 2002;214(1):71–83. DOI: 10.1006/jtbi.2001.2445.
Received: 
28.08.2003
Accepted: 
02.10.2003
Available online: 
23.11.2023
Published: 
31.12.2003
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