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Updated: Jun 5, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Collective phase chaos in the dynamics of interacting oscillator ensembles
Sergey P Kuznetsov1, Arkady Pikovsky, Michael Rosenblum
1Kotel'nikov's Institute of Radio-Engineering and Electronics, RAS, Saratov Branch, Zelenaya Str. 38, Saratov 410019, Russian Federation.
Abstract:
We study the chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is arranged through quadratic nonlinear coupling. We show numerically that in the course of alternating Kuramoto transitions to synchrony and back to asynchrony, the exchange of excitations between two subpopulations proceeds in such a way that their collective phases are governed by an expanding circle map similar to the Bernoulli map. We perform the Lyapunov analysis of the dynamics and discuss finite-size effects.
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