Synchronization by reactive coupling and nonlinear frequency pulling

M. C. Cross*, J. L. Rogers, Ron Lifshitz, A. Zumdieck

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We present a detailed analysis of a model for the synchronization of nonlinear oscillators due to reactive coupling and nonlinear frequency pulling. We study the model for the mean field case of all-to-all coupling, deriving results for the initial onset of synchronization as the coupling or nonlinearity increase, and conditions for the existence of the completely synchronized state when all the oscillators evolve with the same frequency. Explicit results are derived for the Lorentzian, triangular, and top-hat distributions of oscillator frequencies. Numerical simulations are used to construct complete phase diagrams for these distributions.

Original languageEnglish
Article number036205
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number3
StatePublished - 2006


FundersFunder number
Directorate for Mathematical and Physical Sciences0314069


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