De Monte Silvia, d'Ovidio Francesco, Mosekilde Erik
Chaos Group, Department of Physics, Technical University of Denmark, DK 2800 Lyngby, Denmark.
Phys Rev Lett. 2003 Feb 7;90(5):054102. doi: 10.1103/PhysRevLett.90.054102. Epub 2003 Feb 4.
This Letter 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 an approximation, the method allows us to quantitatively study the transitions among the collective 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.
本信函提出了一种方法，通过该方法可以用少数宏观自由度来描述具有参数多样性和全局耦合的动力系统群体的平均场动力学。该方法适用于相干区域内任何规模和功能形式的群体。它要求离散参数呈线性变化或具有窄分布。尽管是一种近似方法，但该方法使我们能够将集体状态之间的转变作为有效宏观自由度的分岔进行定量研究。为了说明这一点，我们研究了具有时间尺度失配的混沌振荡器的振子死亡现象和完全锁定路径。
