Characteristics and synchronization of time-delay systems driven by a common noise
1 Centre for Dynamics of Complex Systems, University of Potsdam, 14469 Potsdam, Germany
2 Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
3 Institute of Physics, Humboldt University, 12489 Berlin, Germany
Revised: 9 August 2010
Published online: 1 October 2010
We investigate the characteristics of time-delay systems in the presence of Gaussian noise. We show that the delay time embedded in the time series of time-delay system with constant delay cannot be estimated in the presence noise for appropriate values of noise intensity thereby forbidding any possibility of phase space reconstruction. We also demonstrate the existence of complete synchronization between two independent identical time-delay systems driven by a common noise without explicitly establishing any external coupling between them.
© EDP Sciences, Springer-Verlag, 2010