1986/09/01 by Hidetsugu Sakaguchi, Yoshiki Kuramoto · 8 citations
paper · doi:10.1143/ptp.76.576
crossref issued 1986/09/01 · crossref published 1986/09/01 · crossref published-online 1986/09/01 · crossref published-print 1986/09/01 · crossref created 2005/12/14 · crossref deposited 2025/07/15 · crossref indexed 2026/07/31
Abstract Some analytical results are obtained for a large population of limit-cycle oscillators modelled by a set of deterministic equations φ = ωi-N-1K ΣNj=1 sin (φi-φj+α) (i=1,2, …, N), where φi is the phase of the i-th oscillator and ωi's are parameters distributed randomly. The present work is a generalization of the previous one where the study was limited to the case of vanishing α and symmetric distribution of ωi. As in the previous case, a particular macroscopic solution of steady rotation is found, which branches off the trivial solution at some positive K. A computer simulation with N=1000 is carried out, which correctly reproduces our analytical results.