Double transition to synchronization: A generic emergent transitional behavior in large systems of coupled oscillators
Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya - Terrassa 08222, Spain, EU
2 University of Maryland - College Park, MD 20742, USA
Accepted: 24 April 2012
We study a system of M≫ 1 nonidentical laser oscillators coupled with time delay through a central laser oscillator in a star-coupling topology. In the large-M limit we show that this system undergoes novel transitional behavior which represents a new generic type of emergent behavior in large systems of coupled laser oscillators. Specifically, we observe a sequence of two dynamical transitions (“a double transition”). A first transition occurs when the effective threshold of the central oscillators is reached leading to an increase of the order parameter to a level far above the noise level. As the control parameter is raised further a second transition occurs leading to a further increase of the order parameter to a level of order M1/2 above the level achieved past the first transition. A scaling analysis and numerical experiments reveal the underlying mechanism of this scenario. We suggest that double transitions, discovered here in the context of a specific system, are expected to occur in diverse situations involving large coupled-oscillator networks.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 05.45.Xt – Synchronization; coupled oscillators
© EPLA, 2012