Coherent regimes of globally coupled dynamical systems

Details Coherent regimes of globally coupled dynamical systems Coherent regimes of globally coupled dynamical systems

2002-07-30

arxiv.org/abs/cond-mat/0207701v2

Phys. Rev. Lett. 90 (2003) 054102

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.90.054102

The paper presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to populations of any size and functional form in the region of coherence. It requires linear variation or a narrow distribution for the dispersed parameter. Although being an approximation, the method allows us to quantitatively study the collective regimes that arise as a result of diversity and coupling and to interpret the transitions among these regimes as bifurcations of the effective macroscopic degrees of freedom. To illustrate, the phenomenon of oscillator death and the route to full locking are examined for chaotic oscillators with time scale mismatch.

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