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

Cite this article as:

Petrov V. S., Osipov G. V. Influence of passive elements on the synchronization of oscillatory ensembles. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 3, pp. 46-59. DOI:


Influence of passive elements on the synchronization of oscillatory ensembles


This paper deals with the influence of the passive elements on the synchronization in the ensembles of coupled non­identical Bonhoeffer–van der Pol oscillators. With a help of numerical experiment it was demonstrated that the introduction of passive elements may lead to both increase and decrease of global synchronization threshold in the system. These results were confirmed analytically using piecewise linear approximation of the Bonhoeffer–van der Pol model. The results obtained for the ensemble of three coupled elements are generalized to the case of two dimensional lattices of non­identical oscillators.


1. Bub G., Shrier A. and Glass L. Spiral wave generation in heterogeneous excitable media // Phys. Rev. Lett. 2002. Vol. 88. 058101. 2. Bub G., Shrier A. and Glass L. Global organization of dynamics in oscillatory heterogeneous excitable media // Phys. Rev. Lett. 2005. Vol. 94. 028105. 3. Blasius B. and Tonjes R.  ? Quasiregular concentric waves in heterogeneous lattices of coupled oscillators // Phys. Rev. Lett. 2005. Vol. 95. 084101. 4. Kheowan O.-U., Mihaliuk E., Blasius B., Sendina-Nadal I. and Showalter K.  ? Wave mediated synchronization of nonuniform oscillatory media // Phys. Rev. Lett. 2007. Vol. 98. 074101. 5. Hwang S., Yea K. and Lee K.J. Complex-periodic spiral waves in confluent cardiac cell cultures induced by localized inhomogeneities // Phys. Rev. Lett. 2004. Vol. 92. 198103. 6. Ten Tusscher K.H.W.J. and Panfilov A.V. // Europace. 2007. Vol. 9. P. 38. 7. Пиковский А.С., Розенблюм М.Г., Куртс Ю. Синхронизация. Фундаментальное нелинейное явление. М: Техносфера, 2003. 8. Pazo D. and Montbri  ? o E.  ? // Phys. Rev. E. 2006. Vol. 73. 055202(R). 9. Bonhoeffer K.F. Modelle der Nervenerregung // Naturwissenschaften. 1953. Vol. 40. P. 301. 10. Kryukov A.K., Petrov V.S., Averyanova L.S., Osipov G.V., Chen W., Drugova O. and Chan C.K. // Chaos. 2008. Vol. 18. 037129.

Short text (in English):
(downloads: 5)
Full text:
(downloads: 8)