E.M. Shahverdiev

Lag synchronization in time-delayed systems

We present the first analytical investigation of lag chaos synchronization between two unidirectionally coupled identical time-delayed systems in the case when these systems are governed by two characteristic times: the delay time in the coupling is generally different from the delay time in the coupled systems. Also, for the first time we demonstrate that parameter mismatches can explain the fact that the lag time is equal to the coupling delay. These findings can be helpful to explain coupling-delay lag time in chaos synchronization.

Parameter mismatches, variable delay times and synchronization in time-delayed systems

We investigate synchronization between two unidirectionally linearly coupled chaotic non-identical time-delayed systems and show that parameter mismatches are of crucial importance to achieve synchronization. We establish that independent of the relation between the delay time in the coupled systems and the coupling delay time, only retarded synchronization with the coupling delay time is obtained. We show that with parameter mismatch or without it neither complete nor anticipating synchronization occurs. We derive existence and stability conditions for the retarded synchronization manifold. We demonstrate our approach using examples of the Ikeda and Mackey-Glass models. Also for the first time we investigate chaos synchronization in time-delayed systems with variable delay time and find both existence and sufficient stability conditions for the retarded synchronization manifold with the coupling delay lag time. Also for the first time we consider synchronization between two unidirectionally coupled chaotic multi-feedback Ikeda systems and derive existence and stability conditions for the different anticipating, lag, and complete synchronization regimes.

Inverse anticipating chaos synchronization.

We report a new type of chaos synchronization:inverse anticipating synchronization, where a time delay chaotic system can drive another system in such a way that the driven system anticipates the driver by synchronizing with its inverse future state. We extend the concept of inverse anticipating chaos synchronization to cascaded systems. We propose means for the experimental observation of inverse anticipating chaos synchronization in external cavity lasers.

Lag times and parameter mismatches in synchronization of unidirectionally coupled chaotic external cavity semiconductor lasers.

We report an analysis of synchronization between two unidirectionally coupled chaotic external cavity master/slave semiconductor lasers with two characteristic delay times, where the delay time in the coupling is different from the delay time in the coupled systems themselves. We demonstrate for the first time that parameter mismatches in photon decay rates for the master and slave lasers can explain the experimental observation that the lag time is equal to the coupling delay time.

Dual and dual-cross synchronizations in chaotic systems

In this paper we investigate dual synchronization and dual-cross synchronization between a transmitter and a receiver, each consisting of two master and slave systems. We demonstrate our approach using the example of synchronization of chaotic external cavity laser diodes. In the synchronization scheme under consideration the joint error signal, which is the difference between the sum of the outputs from the master systems in the transmitter and the sum of outputs from the slave systems in the receiver, is fed into each slave system and synchronizations between the master lasers and slave lasers under possible configurations are studied. By use of error dynamics we derive existence conditions for synchronization between the transmitter and receiver. We find that in all the studied cases synchronization between the transmitter and receiver occurs when the sum of the contributions from individual master (or slave) systems in the transmitter (or receiver) is equal to unity. For the first time we demonstrate that an arbitrarily chosen master system from the transmitter synchronizes with the slave system from the receiver which has an equal contribution weight to the joint error signal. These findings are considered to be of interest in multichannel communication schemes.

CHAOS SYNCHRONIZATION IN MULTIPLE TIME DELAY ELECTROOPTICAL SEMICONDUCTOR LASERS

We make the first report of the chaos synchronization regimes in the unidirectionally-coupled multiple time delay electrooptical semiconductor lasers. We derive the existence and sufficient stability conditions for the synchronization regimes. Analytical results are fully supported by numerical simulations.

Duality of existence conditions for synchronization of unidirectionally coupled chaotic external cavity semiconductor lasers

We find a new existence condition for synchronization between two unidirectionally coupled chaotic external cavity master/slave semiconductor lasers with two characteristic delay times, where the delay time in the coupling is different from the delay time in the coupled systems themselves.

CHAOS SYNCHRONIZATION IN THE MULTIFEEDBACK MACKEY–GLASS MODEL

We investigate synchronization between two unidirectionally coupled chaotic multi-feedback Ikeda systems and find both the existence and stability conditions for anticipating, lag, and complete synchronizations.Generalization of the approach to a wide class of nonlinear systems is also presented.We investigate synchronization between two unidirectionally linearly coupled chaotic multifeedback Mackey–Glass systems and find the existence and stability conditions for complete synchronization. Numerical simulations fully support the theory. We also present generalization of the approach to the wider class of nonlinear systems.

PARAMETER MISMATCHES AND INVERSE SYNCHRONIZATION IN THE IKEDA MODEL

We investigate inverse retarded synchronization between two uni-directionally linearly coupled chaotic non-identical Ikeda models and show that parameter mismatches are of crucial importance to achieve synchronization. We establish that independent of the relation between the delay time in the coupled systems and the coupling delay time, only inverse retarded synchronization with the coupling delay time is obtained. We derive existence and stability conditions for the inverse retarded synchronization manifold. We show that with parameter mismatch or without it neither inverse complete nor inverse anticipating synchronization occurs. Numerical simulations fully support the analytical approach.

Experimental observation of anticipating chaotic synchronisation using external cavity laser diodes

We report the first observation of anticipating synchronisation using a chaotic external cavity laser diode (master) coupled to a solitary laser diode (slave). Experimental conditions are identified for which anticipated synchronisation occurs between the lasers.