Complex dynamics of an oscillator ensemble with uniformly distributed natural frequencies and global nonlinear coupling

Yernur Baibolatov, Michael Rosenblum, Zeinulla Zh. Zhanabaev, Arkady Pikovsky
2010 Physical Review E  
We consider large populations of phase oscillators with global nonlinear coupling. For identical oscillators such populations are known to demonstrate a transition from completely synchronized state to the state of self-organized quasiperiodicity. In this state phases of all units differ, yet the population is not completely incoherent but produces a nonzero mean field; the frequency of the latter differs from the frequency of individual units. Here we analyze the dynamics of such populations
more » ... such populations in case of uniformly distributed natural frequencies. We demonstrate numerically and describe theoretically ͑i͒ states of complete synchrony, ͑ii͒ regimes with coexistence of a synchronous cluster and a drifting subpopulation, and ͑iii͒ self-organized quasiperiodic states with nonzero mean field and all oscillators drifting with respect to it. We analyze transitions between different states with the increase of the coupling strength; in particular we show that the mean field arises via a discontinuous transition. For a further illustration we compare the results for the nonlinear model with those for the Kuramoto-Sakaguchi model.
doi:10.1103/physreve.82.016212 pmid:20866712 fatcat:gt65lzj5grbevbnvejdm3tc72y