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Discontinuity, Nonlinearity, and Complexity 1(3) (2012) 253--261 | DOI:10.5890/DNC.2012.07.001

Vladimir V. Klinshov; Vladimir I. Nekorkin

Institute of Applied Physics, Nizhny Novgorod, Russia

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Abstract

In this paper we study the global synchronization in the ensembles of time-delay coupled pulse oscillators. We prove that the stability of the synchronization regime depends on the fulfillment of the simple inequality for the derivative of the phase reset curve. This finding is checked by numerical simulations which confirm the above inequality to be the sufficient condition for the synchronization. In the case of sin-shape phase reset curve it results in a stripped structure of the parameter space in which the areas with and without synchronic state alternate with the growth of the coupling delay.

Acknowledgments

The authors acknowledge the support from RFBR (grants No. 09-02-00719, 09-02-91061, 10-02-00643) and the Federal Target Program “Academic and teaching staff of innovative Russia” for 2009-2013 years (contracts No. P942, P1225, 02.740.11.5188, 14.740.11.0348).

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