AUTORESET OF PHASE AND OSCILLATORY ACTIVITY PATTERNS IN AUTOOSCILLATORY MODELS OF NEURONAL SYSTEMS
Cite this article as:
Kazantsev V. B., Nekorkin . 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: https://doi.org/10.18500/0869-6632-2005-13-4-56-72
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.
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. Vol. 1250. P. 409.
3. Behrendt R.P. Hallucinations: Synchronisation of thalamocortical c oscillations underconstrained by sensory input // Consciousness and Cognition. 2003. Vol. 12. P. 413.
4. Leznik E., Makarenko V.I., Llinas R. Electrotonically mediated oscillatory patterns in neuronal ensembles: An In Vitro Voltage-Dependent Dye-Imaging Study in the Inferior Olive // J. Neurosci. 2002. Vol. 22. P. 2804.
5. Welsh J.P., Llinas R. Some organizing principles for the control of movement based on olivocerebellar physiology / Eds. de Zeeuw C. I., Strata P. and Voodg // Progress in Brain Research. 1997. Vol. 114.
6. Henze D.A., Buzsak G. Single cell contributions to network activity in the hippocampus //International Congress Series. 2003. 1250. P. 161.
7. Magee J.C. A prominent role for intrinsic neuronal properties in temporal coding // Trends Neurosci. 2003. Vol. 26, No1. P. 14.
8. Kazantsev V.B., Nekorkin V.I., Makarenko V.I., Llinas R. Olivo-cerebellar clusterbased universal control system // Procs. Natl. Acad. Sci. USA. 2003. Vol. 100 (22). P. 13064.
9. Андронов А.А., Витт А.А., Хайкин С.Э. Теория колебаний. М.: Физматизд, 1959. 916 c.
10. Пиковский А., Розенблюм М., Куртс Ю. Синхронизация. Фундаментальное нелинейное явление. М.: Техносфера, 2003. 496 с.
11. Гласс Л., Мэкки М. От часов к хаосу. Ритмы жизни. М.: Мир, 1991. 248 с.
12. FitzHugh R. Mathematical models of excitation and propagation in nerve. In Biological Engineering (Ed. H.P. Schwan). 1969. 1-85.
13. Казанцев В.Б., Некоркин В.И. Динамика колебательных нейронов. Информационные аспекты // Нелинейные волны – 2002. Нижний Новгород: ИПФ РАН, 2003. 29 c.
14. Казанцев В.Б., Некоркин В.И. Фазово-управляемые колебания в нейродинамике // Нелинейные волны – 2004. Нижний Новгород: ИПФ РАН, 2005. С. 345.
15. Kazantsev V.B., Nekorkin V.I., Makarenko V.I., Llinas R. Self-referential phase reset based on inferior olive oscillator dynamics // Proc. Natl. Acad. Sci. USA. 2004. Vol. 101, No 52. P. 18183.
16. Lang E.J., Sugihara I., Welsh J.P., Llinas R. Patterns of spontaneous Purkinje cell complex spike activity in the awake rat // J. Neurosci. 1999. Vol. 19(7) P. 2728.
17. Hoppensteadt F.C., Izhikevich E.M. Oscillatory neurocomputers with dynamic connectivity // Phys. Rev. Lett. 1999. Vol. 82. P. 2983.
18. Llinas R., Baker R., Sotelo C. Electrotonic coupling between neurons in cat inferior olive // J. Neurophysiol. 1974. Vol. 37. P. 560.
19. Hopfield J. J. Neurons with graded response have collective computational properties like those of two-state neurons // Proc. Natl. Acad. Sci. USA. 1984. Vol. 81. P. 3088.
BibTeX
author = {V. B. Kazantsev and Vladimir I. Nekorkin},
title = {AUTORESET OF PHASE AND OSCILLATORY ACTIVITY PATTERNS IN AUTOOSCILLATORY MODELS OF NEURONAL SYSTEMS},
year = {2005},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {13},number = {4},
url = {https://old-andjournal.sgu.ru/en/articles/autoreset-of-phase-and-oscillatory-activity-patterns-in-autooscillatory-models-of-neuronal},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2005-13-4-56-72},pages = {56--72},issn = {0869-6632},
keywords = {-},
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. }}