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


For citation:

Mishchenko M. A., Shalfeev V. D., Matrosov V. V. Neuron-like dynamics in phase-locked loop. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 4, pp. 122-130. DOI: 10.18500/0869-6632-2012-20-4-122-130

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text:
Language: 
Russian
Article type: 
Article
UDC: 
537.86; 001.891.573; 51.76

Neuron-like dynamics in phase-locked loop

Autors: 
Mishchenko Mikhail Andreevich, Lobachevsky State University of Nizhny Novgorod
Shalfeev Vladimir Dmitrievich, Lobachevsky State University of Nizhny Novgorod
Matrosov Valerij Vladimirovich, Lobachevsky State University of Nizhny Novgorod
Abstract: 

Use of phase-locked loop as a model of neuron-like element is discussed. Parameter space of the model is partitioned into areas of different regimes specific for dynamics of real neurons. Bifurcation mechanisms of transitions between regimes are examined.

Reference: 
  1. Rabinovich MI, Varona P, Selverston AI, Abarbanel HDI. Dynamical principles in neuroscience. Reviews of Modern Physics. 2006;78(4):1213–1265. DOI: 10.1103/RevModPhys.78.1213.
  2. Izhikevich EM. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. Cambridge, The MIT Press; 2007. 464 p.
  3. Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology. 1952;117(4):500–544. DOI: 10.1113/jphysiol.1952.sp004764.
  4. Cohen AH, Holmes PJ, Rand RH. The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model. Journal of Mathematical Biology. 1982;13(3):345–369. DOI: 10.1007/bf00276069.
  5. Kazanovich YB, Krukov VI, Lyuzyanina TB. Synchronization via phase locking in oscillatory models of neural networks. In: Neurocomputers and Attention. Neurobiology, Synchronisation and Chaos. Manchester: Manchester University Press; 1991. P. 269–284.
  6. Abarbanel HD, Rabinovich MI, Selverston A, Bazhenov MV, Huerta R, Sushchik MM, Rubchinskii LL. Synchronisation in neural networks. Phys. Usp. 1996;39(4):337–362. DOI: 10.1070/PU1996v039n04ABEH000141.
  7. Mishchenko MA. Neuron-like model based on phase-locked loop system. Vestnik of Lobachevsky University of Nizhni Novgorod. 2011;5(3):279–282 (in Russian).
  8. Shakhgildyan VV, Lyakhovkin AA. Phase Locking Systems. Moscow: Svyaz; 1972. 448 p. (in Russian).
  9. Lindsey V. Synchronization Systems in Communication and Control. Prentice-Hall; 1972. 704 p.
  10. Kapranov MV. Elements of the Theory of Phase Synchronization Systems. Oscillation Theory Course Study Guide. Moscow: MPEI Publishing; 2006. 208 p. (in Russian).
  11. Shalfeev VD. Investigation of the dynamics of a system of automatic phase control of frequency with a coupling capacitor in the control loop. Radiophys. Quantum Electron. 1968;11(3):221–226. DOI: 10.1007/BF01033800.
  12. Bakunov GM, Matrosov VV. Complex and chaotic oscillations in the PLL system with a separating capacitor in the control circuit. In: Proceedings of the XIII Scientific Conference on Radiophysics dedicated to the 85th anniversary of the birth of M.A. Miller. Nizhny Novgorod, 7 May 2009. Nizhny Novgorod: UNN; 2009. P. 65–67 (in Russian).
  13. Zhu JJ, Connors BW. Intrinsic firing patterns and whisker–evoked synaptic responses of neurons in the rat barrel cortex. Journal of Neurophysiology. 1999;81(3):1171–1183. DOI: 10.1152/jn.1999.81.3.1171.
  14. Neimark YI, Landa PS. Stochastic and Chaotic Oscillations. Dordrecht: Springer; 1992. 500 p. DOI: 10.1007/978-94-011-2596-3.
  15. Matrosov VV, Shmelev AV. Nonlinear dynamics of a ring of two coupled phase locked loops. Izvestiya VUZ. Applied Nonlinear Dynamics. 2010;18(4):67–80 (in Russian). DOI: 10.18500/0869-6632-2010-18-4-67-80.
Received: 
30.03.2012
Accepted: 
30.03.2012
Published: 
31.10.2012
Short text (in English):
(downloads: 58)