Integrable order parameter dynamics of globally coupled oscillators
arXiv:1606.02526 · doi:10.1088/1751-8113/49/6/065101
Abstract
We study the nonlinear dynamics of globally coupled nonidentical oscillators in the framework of two order parameter (mean field and amplitude-frequency correlator) reduction. The main result of the paper is the exact solution of the corresponding nonlinear system on an attracting manifold. We present a complete classification of phase portraits and bifurcations, obtain explicit expressions for invariant manifolds (a limit cycle among them) and derive analytical solutions for arbitrary initial data and different regimes.
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