The Kuramoto model with distributed shear
Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria - 39005 Santander, Spain, EU
2 Department of Information and Communication Technologies, Universitat Pompeu Fabra 08003 Barcelona, Spain, EU
Accepted: 9 August 2011
We uncover a solvable generalization of the Kuramoto model in which shears (or nonisochronicities) and natural frequencies are distributed and statistically dependent. We show that the strength and sign of this dependence greatly alter synchronization and yield qualitatively different phase diagrams. The Ott-Antonsen ansatz allows us to obtain analytical results for a specific family of joint distributions. We also derive, using linear stability analysis, general formulae for the stability border of incoherence.
PACS: 05.45.Xt – Synchronization; coupled oscillators
© EPLA, 2011