Abstract
We study the effect of nonuniform delay coupling due to degree inhomogeneity in a system of identical Kuramoto oscillators on a bipartite network with the star topology. The hub and peripheral oscillators have synchronized solutions with phase shift between them. Transcendental equations are obtained for the collective frequencies and phase shifts, and linear stability conditions are derived for the solutions. Numerical simulations are in good agreement with these results. Systems in which collective frequencies depend on both delays and phase shifts are important in the context of optimizing synchronization rates.
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