Entrainment of complex oscillator networks

Dynamics of random oscillator networks partly forced by a external pacemaker is numerically investigated. We find that the entrainment frequency window of a network decreases exponentially with its depth, defined as the mean forward distance of the elements from the pacemaker. Effectively, only shallow networks have the ability to be entrained by the pacemaker. The exponential dependence is also derived analytically as an approximation for large random asymmetric networks.