Synchronization in networks of chaotic systems with time-delay coupling.
In this paper, we consider synchronization of N identical nonlinear systems unidirectionally or bidirectionally coupled with time delay. First we show, using the small-gain theorem, that trajectories of coupled strictly semi-passive systems converge to a bounded region. Next, we consider the network structure under which the synchronization error dynamics has a trivial solution at zero and derive a necessary condition for synchronization with respect to the network structure. Using these facts, we then derive sufficient conditions for synchronization of the systems in terms of linear matrix inequalities via the Lyapunov-Krasovskii functional approach. The obtained results are illustrated on networks of Lorentz systems with coupling delay.
Oguchi
Toshiki
T
Department of Mechanical Engineering, Graduate School of Science and Engineering, Tokyo Metropolitan University, 1-1, Minami-Osawa, Hachioji-shi, Tokyo 192-0397, Japan.
Nijmeijer
Henk
H
Yamamoto
Takashi
T
D000465:Algorithms; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D005246:Feedback; D053858:Metabolic Networks and Pathways / Q000502:physiology*; D008962:Models, Theoretical; D009415:Nerve Net / Q000502:physiology*; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*