Dynamical clustering in oscillator ensembles with time-dependent interactionsD. H. Zanette1, 2 and A. S. Mikhailov1
1 Fritz Haber Institut der Max Planck Gesellschaft, Abteilung Physikalische Chemie Faradayweg 4-6, 14195 Berlin, Germany
2 Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche and Instituto Balseiro - 8400 Bariloche, Río Negro, Argentina
(Received 13 August 2003; accepted in final form 5 December 2003)
We consider an ensemble of coupled oscillators whose individual states, in addition to the phase, are characterized by an internal variable with autonomous evolution. The time scale of this evolution is different for each oscillator, so that the ensemble is inhomogeneous with respect to the internal variable. Interactions between oscillators depend on this variable and thus vary with time. We show that, as the inhomogeneity of time scales in the internal evolution grows, the system undergoes a critical transition between ordered and incoherent states. This transition is mediated by a regime of dynamical clustering, where the ensemble recurrently splits into groups formed by varying subpopulations.
05.45.Xt - Synchronization; coupled oscillators.
89.75.Fb - Structures and organization in complex systems.
05.70.Fh - Phase transitions: general studies.
© EDP Sciences 2004