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


For citation:

Kryukov A. K., Osipov G. V. Oscillatory media properties influence on excitation propagation. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 2, pp. 188-200. DOI: 10.18500/0869-6632-2013-21-2-188-200

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
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Language: 
Russian
Article type: 
Article
UDC: 
621.391.01

Oscillatory media properties influence on excitation propagation

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

We study synchronization in ensembles of locally diffusive coupled Bonhoeffer–van der Pol oscillators. Individual elements frequencies influence on excitation propagation in one- and two-dimensional media is investigated. We show that excitation propagation speed depends on frequency mismatch between synchronization frequency and elements’ individual frequencies. Qualitative and quantitative results describing this effect are numerical modeling data and analytical research.

Reference: 
  1. Osipov GV, Kurths J, Zhou Ch. Synchronization in Oscillatory Networks. Berlin: Springer Verlag; 2007. 372 p.
  2. Pikovsky AS, Rosenblum MG, Kurts Yu. Synchronization. A fundamental nonlinear phenomenon.Moscow: Tehnosphera; 2003. 496 p. (In Russian).
  3. Osipov GV, Sushchik MM. Synchronized clusters and multistability in arrays of oscillators with different natural frequencies. Phys. Rev. E. 1998;58(6):7198.
  4. Torre V. A theory of synchronization of heart pace-maker cells, J. Theor. Biol.1976;61(1):55–71. DOI: 10.1016/0022-5193(76)90104-1.
  5. Kryukov AK, Petrov VS, Averyanova LS, Osipov GV, Chen W, Drugova O, Chan CK. Synchronization phenomena in mixed media of passive, excitable and oscillatory cells. Chaos. 2008;18(3):037129. DOI: 10.1063/1.2956985.
  6. Bonhoeffer KF. Models of nerve excitation. Naturwissenschaften. 1953;40:301–311.
  7. Zykov VS. Analytical dependence of excitation wave velocity in two-dimensional excitable medium on curvature of front. Biophysics. 1980;25:888–895.
  8. Kryukov AK, Osipov GV, Polovinkin AV, Kurths J. Synchronous regimes in ensembles of coupled Bonhoeffer–van der Pol oscillators. Phys. Rev. E. 2009;79(4):046209. DOI:10.1103/PHYSREVE.79.046209.
  9. Krjukov AK, Osipov GV, Polovinkin AV. Variety of synchronous regimes in ensembles of nonidentical oscillators: two coupled elements. Izvestiya VUZ. Applied Nonlinear Dynamics. 2009;17(2):16-28. DOI: 10.18500/0869-6632-2009-17-2-16-28.
  10. Krjukov AK, Osipov GV, Polovinkin AV. Variety of synchronous regimes in ensembles of nonidentical oscillators: chain and lattice. Izvestiya VUZ. Applied Nonlinear Dynamics. 2009;17(2):29-36. DOI: 10.18500/0869-6632-2009-17-2-29-36.
  11. Diamant NE, Rose PK, Davidson EJ. Computer simulation of intestinal slowwave frequency gradient. Am. J. Physiol. 1970;219(6):1684–1690. DOI:10.1152/AJPLEGACY.1970.219.6.1684.
  12. Fundamental and clinical physiology. Ed. Kamkina A., Kamenskiy A. Moscow: Akademiya. 2004. 1072 p. (In Russian).
Received: 
06.08.2012
Accepted: 
11.12.2012
Published: 
31.07.2013
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