1998/07/30 by J. M. G. Vilar, Vilar, J. M. G., A. Corral +1
Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9807403
4 pages, 2 figures
arxiv created 1998/07/30 · arxiv updated 2009/11/30
We explore systems of pulse-coupled oscillators beyond the mean-field limit [R.E. Mirollo and S.H. Strogatz, SIAM J. Appl. Math. \bf 50, 1645 (1990)] by means of a manageable description which leads to a great simplification of the dynamics. Sufficient conditions for synchronization are exactly obtained for a ring with nearest-neighbor directed interactions, turning out to be the same as in the all-to-all case. Our analysis shows new synchronization mechanisms occurring when the interactions are local.