Winding Numbers and Average Frequencies in Phase Oscillator Networks

摘要: We study networks of coupled phase oscillators and show that network architecture can force relations between average frequencies the oscillators. The main tool our analysis is cell theory developed by Stewart, Golubitsky, Pivato, Torok, which provides precise corresponding class ODEs in RM gives conditions for flow-invariance certain polydiagonal subspaces all systems with a given architecture. generalizes notion fixed-point subgroups symmetries directly extends to For (but not generally RM, where M ? 2), invariant subsets codimension one arise naturally strongly restrict dynamics. say two i j coevolve if ?i = ?j flow-invariant, these must be equal. Given architecture, it shown direct way testing how coevolving form collections closely related give generalization results synchronous clusters using quotient networks, discuss implications spiking cells those connected through buffers implement coupling