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


For citation:

Kazantsev V. B., Nekorkin V. I. Autoreset of phase and oscillatory activity patterns in autooscillatory models of neuronal systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2005, vol. 13, iss. 4, pp. 56-72. DOI: 10.18500/0869-6632-2005-13-4-56-72

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 150)
Language: 
Russian
Article type: 
Article
UDC: 
621.373.1

Autoreset of phase and oscillatory activity patterns in autooscillatory models of neuronal systems

Autors: 
Kazantsev Viktor Borisovich, Institute of Applied Physics of the Russian Academy of Sciences
Nekorkin Vladimir Isaakovich, Institute of Applied Physics of the Russian Academy of Sciences
Abstract: 

The processes of oscillatory pattern formation in autooscillatory neuronal models are investigated. Such patterns play a key role in the information processes used in higher brain functions. The effect of pulse-induced phase autoreset in the model of neurons with subthreshold oscillations is studied. As a result of this effect the reset phase value does not depend on the initial phase. It is defined only by the stimulus parameters. The autoreset effect can be used for phase synchronization and phase cluster formation in ensembles of autooscillatory units. To sustain the inter-unit phase relations it is proposed to use the mechanism of pulse-controlled coupling between neuronal elements with subthreshold oscillations. The model is developed on the base of the dynamics of olivo-cerebellar neuronal system responsible for motor pattern formation in the brain.

Key words: 
Reference: 
  1. Llinas R. I of the Vortex. From Neurons to Self. The MIT Press Cambridge, Massachusetts; 2002. 302 p.
  2. Llinas R. Consciousness and the thalamocortical loop. International Congress Series. 2003;1250:409–416. DOI: 10.1016/S0531-5131(03)01067-7.
  3. Behrendt RP. Hallucinations: Synchronization of thalamocortical c oscillations underconstrained by sensory input. Consciousness and Cognition. 2003;12(3):413–451. DOI: 10.1016/s1053-8100(03)00017-5.
  4. Leznik E, Makarenko VI, Llinas R. Electrotonically mediated oscillatory patterns in neuronal ensembles: An in vitro voltage-dependent dye-imaging study in the inferior olive. J. Neurosci. 2002;22(7):2804–2815. DOI: 10.1523/jneurosci.22-07-02804.2002.
  5. Welsh JP, Llinas R. Some organizing principles for the control of movement based on olivocerebellar physiology. Progress in Brain Research. 1997;114:449–461. DOI: 10.1016/s0079-6123(08)63380-4.
  6. Henze DA, Buzsak G. Single cell contributions to network activity in the hippocampus. International Congress Series. 2003;1250:161–181. DOI: 10.1016/S0531-5131(03)01049-5.
  7. Magee JC. A prominent role for intrinsic neuronal properties in temporal coding. Trends Neurosci. 2003;26(1):14–16. DOI: 10.1016/S0166-2236(02)00012-7.
  8. Kazantsev VB, Nekorkin VI, Makarenko VI, Llinas R. Olivo-cerebellar cluster-based universal control system. Proc. Natl. Acad. Sci. USA. 2003;100(22):13064–13068. DOI: 10.1073/pnas.1635110100.
  9. Andronov AA, Vitt AA, Khaikin SE. Theory of Oscillators. Pergamon Press; 1966. 848 p.
  10. Pikovsky A, Rosenblum M, Kurths J. Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge, UK: Cambridge University Press; 2001. 411 p. DOI: 10.1017/CBO9780511755743.
  11. Glass L, Mackey MC. From Clocks to Chaos: The Rhythms of Life. Princeton: Princeton University Press; 1988. 272 p.
  12. FitzHugh R. Mathematical models of excitation and propagation in nerve. In: Schwan HP, editor. Biological Engineering. New York: McGraw Hill; 1969. P. 1–85.
  13. Kazantsev VB, Nekorkin VI. Dynamics of oscillatory neurons. Information aspects. In: Nonlinear Waves - 2002. Nizhny Novgorod: IAP RAS; 2003. P. 9–33 (in Russian).
  14. Kazantsev VB, Nekorkin VI. Phase-controlled oscillations in neurodynamics. In: Nonlinear Waves - 2004. Nizhny Novgorod: IAP RAS; 2005. P. 345–361 (in Russian).
  15. Kazantsev VB, Nekorkin VI, Makarenko VI, Llinas R. Self-referential phase reset based on inferior olive oscillator dynamics. Proc. Natl. Acad. Sci. USA. 2004;101(52):18183–18188. DOI: 10.1073/pnas.0407900101.
  16. Lang EJ, Sugihara I, Welsh JP, Llinas R. Patterns of spontaneous Purkinje cell complex spike activity in the awake rat. J. Neurosci. 1999;19(7):2728–2739. DOI: 10.1523/jneurosci.19-07-02728.1999.
  17. Hoppensteadt FC, Izhikevich EM. Oscillatory neurocomputers with dynamic connectivity. Phys. Rev. Lett. 1999;82(14):2983–2986. DOI: 10.1103/PhysRevLett.82.2983.
  18. Llinas R, Baker R, Sotelo C. Electrotonic coupling between neurons in cat inferior olive. J. Neurophysiol. 1974;37(3):560–571. DOI: 10.1152/jn.1974.37.3.560.
  19. Hopfield JJ. Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. USA. 1984;81(10):3088–3092. DOI: 10.1073/pnas.81.10.3088.
Received: 
15.07.2005
Accepted: 
15.07.2005
Published: 
30.11.2005
Short text (in English):
(downloads: 66)