Note: This content is accessible to all versions of every browser. However, this browser does not seem to support current Web standards, preventing the display of our site's design details.


Obtaining certificates for complete synchronisation of coupled oscillators.


E. August, Mauricio Barahona

Physica D, vol. 240, no. 8, pp. 795-803

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.

Further Information

Type of Publication:


No Files for download available.
% Autogenerated BibTeX entry
@Article { AugBar:2011:IFA_3730,
    author={E. August and Mauricio Barahona},
    title={{Obtaining certificates for complete synchronisation of
	  coupled oscillators.}},
    journal={Physica D},
Permanent link