In order to discover generic effects of heterogeneous communication delays on the dynamics of large systems of coupled oscillators, this Letter studies a modification of the Kuramoto model incorporating a distribution of interaction delays. Corresponding to the case of a large number $N$ of oscillators, we consider the continuum limit (i.e., $N\to \infty$). By focusing attention on the reduced dynamics on an invariant manifold of the original system, we derive governing equations for the system which we use to study the stability of the incoherent states and the dynamical transitional behavior from stable incoherent states to stable coherent states. We find that spread in the distribution function of delays can greatly alter the system dynamics.

• Received 6 March 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.044101