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Abstract: We study a model of coupled oscillators with bidirectional first nearestneighbours coupling with periodic boundary conditions. We show that a stablephase-locked solution is decided by the oscillators at the borders between themajor clusters, which merge to form a larger one of all oscillators at thestage of complete synchronization. We are able to locate these four oscillatorsas well as the size of major clusters in the vicinity of the stage of fullsynchronization which we show to depend only on the set of initial frequencies.Using the method presented here, we are able to obtain an analytic form of thecritical coupling, at which the complete synchronization state occurs.



Author: Hassan F. El-Nashar, Hilda A. Cerdeira

Source: https://arxiv.org/







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