Propagation of small perturbations in synchronized oscillator networksD. H. Zanette
Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche and Instituto Balseiro - 8400 Bariloche, Río Negro, Argentina
received 12 March 2004; accepted in final form 8 September 2004
published online 9 October 2004
We study the propagation of a harmonic perturbation of small amplitude on a network of coupled identical phase oscillators prepared in a state of full synchronization. The perturbation is externally applied to a single oscillator, and is transmitted to the other oscillators through coupling. Numerical results and an approximate analytical treatment, valid for random and ordered networks, show that the response of each oscillator is a rather well-defined function of its distance from the oscillator where the external perturbation is applied. For small distances, the system behaves as a dissipative linear medium: the perturbation amplitude decreases exponentially with the distance, while propagating at constant speed. We suggest that the pattern of interactions may be deduced from measurements of the response of individual oscillators to perturbations applied at different nodes of the network.
05.65.+b - Self-organized systems.
05.45.Xt - Synchronization; coupled oscillators.
45.30.+s - General linear dynamical systems.
© EDP Sciences 2004