In this letter we consider a prototype model which is described as an autonomous continuous time delayed differential equation with just one variable. The chaos has been investigated with variable delay time and the synchronization phenomenon is examined both numerically and analytically using the Krasovskii-Lyapunov functions. We have applied adaptive coupling law for synchronization,where the...

-This paper addresses compensation of dealys within a multi-input-multi-output discrete-time feedback loop for application to real-time distributed control systems. The delay compensation algorithm, formulated, in this paper, is an extension of the standard loop transfer recovery (LTR) procedure from one-step prediction to the general case of p-step prediction ( p > l ) . It is shown that the s...

We compute Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in delay-differential equations with large time delay. We find that characteristic LVs, and backward (Gram-Schmidt) LVs, exhibit long-range correlations, identical to those already observed in dissipative extended systems. In addition we give numerical and theoretical support to the hypothesis that the main LV bel...

Using a simple nonlinear filter, it is possible to shift arbitrarily complex wave forms produced by systems with a delayed feedback backwards in time. Physically, this corresponds to a seemingly noncausal transmission of signals. Filter chains allow for signals travelling against the coupling direction of the chain. These apparent paradoxes are resolved, and possible physical implications are d...

Time delays are ubiquitous in real world and are often sources of complex behaviors of dynamical systems. This paper addresses the problem of parameters identification and synchronization of uncertain chaotic delayed systems subject to time-varying delay. Firstly, a novel and systematic adaptive scheme of synchronization is proposed for delayed dynamical systems containing uncertainties based o...