Synchronization of coupled nonlinear oscillators with shifted gamma-distributed delays

We derive conditions for the synchronization of coupled nonlinear oscillators affected by distributed delays in the interconnections. The distributed delays are characterized by a gamma-distribution kernel with a gap. The approach is based on the stability analysis of synchronized equilibria in the (delays, gain) parameter space and the characterization of the structure of the emanating solutions at the bifurcations. The results are applied to networks of coupled Lorenz system. In particular it is shown that, independently of the network topology, for sufficiently large coupling gains the distribution of the delay has a stabilizing effect on the stability of the synchronized equilibrium.