Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators

Details Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators

2008-06-02

arxiv.org/abs/0806.0004v1

Nonlinear Sciences

Chaotic Dynamics

resubmission of Tex files

Scientific paper

10.1063/1.2930766

It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered. For example, an exact, closed form solution for the nonlinear time evolution of the Kuramoto problem with a Lorentzian oscillator frequency distribution function is obtained. Low dimensional behavior is also demonstrated for several prototypical extensions of the Kuramoto model, and time-delayed coupling is also considered.

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