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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.
Current reversal is an intriguing phenomenon that has been central to recent experimental and theoretical investigations of transport based on ratchet mechanism. By considering a system of two interacting ratchets, we demonstrate how the coupling can be used to control the reversals. In particular, we find that current reversal that exists in a single driven ratchet system can ultimately be eliminated with the presence of a second ratchet. For specific coupling strengths a current-reversal free regime has been detected. Furthermore, in the fully synchronized state characterized by the coupling threshold k(th), a specific driving amplitude a(opt) is found for which the transport is optimum.
We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. We have confirmed these results by estimating instantaneous phases including phase difference, average phase, average frequency, frequency ratio, and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non-phase-coherent attractors. The results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non-phase-coherent attractors directly without explicitly introducing the measure of phase.