Dynamical systems with time-dependent coupling: Clustering and critical behaviour

Details Dynamical systems with time-dependent coupling: Clustering and critical behaviour Dynamical systems with time-dependent coupling: Clustering and critical behaviour

2004-03-02

arxiv.org/abs/cond-mat/0403081v1

Physics

Condensed Matter

Statistical Mechanics

to appear in Physica D

Scientific paper

10.1016/j.physd.2004.03.002

We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with autonomous dynamics. The system exhibits different dynamical regimes, with various forms of collective organization, controlled by the range of interactions and the dispersion of time scales in the evolution of the internal variables. In the limit of large interaction ranges, it reduces to an ensemble of coupled identical phase oscillators and, to some extent, admits to be treated analytically. We find and characterize a transition between ordered and disordered states, mediated by a regime of dynamical clustering.

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