Abstract
This paper focuses on the origin of rich dynamics in a frequency-weighted Kuramoto-oscillator network, which embeds the periodical activity patterns of human beings to understand the collective behaviorial dynamics in human population. We present analytical results of the dynamics of the model by reducing the N-dimensional system to solvable low-dimensional equations. The bifurcation analysis reveals that there exist supercritical Hopf bifurcation and infinite-period saddle-node bifurcation, which explain the rich dynamics including the incoherent, oscillatory, and synchronous states observed in this model.
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