Synchronisation of time--delay systems

Details Synchronisation of time--delay systems Synchronisation of time--delay systems

1999-07-30

arxiv.org/abs/chao-dyn/9908003v1

Phys. Rev. E {\bf 58} (1998) R4072

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevE.58.R4072

We present the linear-stability analysis of synchronised states in coupled time-delay systems. There exists a synchronisation threshold, for which we derive upper bounds, which does not depend on the delay time. We prove that at least for scalar time-delay systems synchronisation is achieved by transmitting a single scalar signal, even if the synchronised solution is given by a high-dimensional chaotic state with a large number of positive Lyapunov-exponents. The analytical results are compared with numerical simulations of two coupled Mackey-Glass equations.

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