Obtaining certificates for complete synchronisation of coupled oscillators

PHYSICA D-NONLINEAR PHENOMENA

卷:240

Article

August, Elias¹  Barahona, Mauricio^2,3 

[1] ETH, Dept Elect Engn, CH-8092 Zurich, Switzerland

[2] Univ London Imperial Coll Sci Technol & Med, Dept Bioengn, London SW7 2AZ, England

[3] Univ London Imperial Coll Sci Technol & Med, Inst Math Sci, London SW7 2AZ, England

关键词: Lyapunov theory;    Contraction theory;    Bendixson's Criterion for higher dimensions;    Semidefinite programming;    Sum of squares decomposition;    Synchronisation of coupled oscillators;   

DOI  :  10.1016/j.physd.2010.12.008

来源: Elsevier

【 摘 要 】

In this paper, we provide a novel reformulation of sufficient conditions that guarantee global complete synchronisation of coupled identical oscillators to make them computationally implementable. To this end, we use semidefinite programming techniques. For the first time, we can efficiently search for and obtain certificates for synchronisability and, additionally, also optimise associated cost functions. In this paper, a Lyapunov-like function (certificate) is used to certify that all trajectories of a networked system consisting of coupled dynamical systems will eventually converge towards a common one, which implies synchronisation. Moreover, we establish new conditions for complete synchronisation, which are based on the so called Bendixson's Criterion for higher dimensional systems. This leads to major improvements on the lower bound of the coupling constant that guarantees global complete synchronisation. Importantly, the certificates are obtained by analysing the connection network and the model representing an individual system only. In order to illustrate the strength of our method we apply it to a system of coupled identical Lorenz oscillators and to coupled van der Pol oscillators. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free