The emergence of coherence in complex networks of heterogeneous dynamical systems

Details The emergence of coherence in complex networks of heterogeneous dynamical systems The emergence of coherence in complex networks of heterogeneous dynamical systems

2006-01-27

arxiv.org/abs/cond-mat/0601639v2

Physical Review Letters 96, 128101 (2006).

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 1 figure. Published version

Scientific paper

10.1103/PhysRevLett.96.254103

We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic, and applies generally to networks for which the number of connections per node is large. We find that the critical coupling strength at which a transition to synchrony takes place depends separately on the dynamics of the individual uncoupled systems and on the largest eigenvalue of the adjacency matrix of the coupling network. Our theory directly generalizes the Kuramoto model of equal strength, all-to-all coupled phase oscillators to the case of oscillators with more realistic dynamics coupled via a large heterogeneous network.

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