Generalized Synchronization Regime Research Articles

Intermittent generalized synchronization and modified system approach: Discrete maps.

The present work deals with the intermittent generalized synchronization regime observed near the boundary of generalized synchronization. The intermittent behavior is considered in the context of two observable phenomena, namely, (i) the birth of the asynchronous stages of motion from the complete synchronous state and (ii) the multistability in detection of the synchronous and asynchronous states. The mechanisms governing these phenomena are revealed and described in this paper with the help of the modified system approach for unidirectionally coupled model oscillators with discrete time.

On existence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with complex topology of attractor

Aim of this work is to study the possibility of existence of multistability near the boundary of generalized synchronization in systems with complex attractor topology. Unidirectionally coupled Lorentz systems have been chosen as an object of study, and a modified auxiliary system method has been used to detect the presence of the synchronous regime. Result of the work is a proof of the presence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with a complex topology of attractor. For this purpose, the basins of attraction of the synchronous and asynchronous states of interacting Lorenz systems have been obtained for the value of the coupling parameter corresponding to the realization of the intermittent generalized synchronization regime in the system under study, and the dependence of the multistability measure on the value of the coupling parameter has also been calculated. It is shown that in the regime of intermittent generalized synchronization the measure of multistability turns out to be positive, which is an additional confirmation of the presence of multistability in this case.

On multistability near the boundary of generalized synchronization in unidirectionally coupled chaotic systems.

Multistability in the intermittent generalized synchronization regime in unidirectionally coupled chaotic systems has been found. To study such a phenomenon, the method for revealing the existence of multistable states in interacting systems being the modification of an auxiliary system approach has been proposed. The efficiency of the method has been testified using the examples of unidirectionally coupled logistic maps and Rössler systems being in the intermittent generalized synchronization regime. The quantitative characteristic of multistability has been introduced into consideration.

Intermittent route to generalized synchronization in bidirectionally coupled chaotic oscillators.

The type of transition from asynchronous behavior to the generalized synchronization regime in mutually coupled chaotic oscillators has been studied. To separate the epochs of the synchronous and asynchronous motion in time series of mutually coupled chaotic oscillators, a method based on the local Lyapunov exponent calculation has been proposed. The efficiency of the method has been testified using the examples of unidirectionally coupled dynamical systems for which the type of transition is well known. The transition to generalized synchronization regime in mutually coupled systems has been shown to be an on-off intermittency as well as in the case of the unidirectional coupling.

Метод определения характеристик перемежающейся обобщенной синхронизации на основе расчета локальных показателей Ляпунова

Method for the laminar and turbulent phase detection in coupled dynamical systems being near the boundary of the generalized synchronization regime based on the calculation of local Lyapunov exponents has been proposed. The efficiency of the method has been testified using the systems with unidirectional coupling allowing the analysis of intermittency by the auxiliary system approach. The results of both methods have been compared with each other, a good agreement between them has been obtained.

Корректность определения характеристик перемежающейся обобщенной синхронизации при использовании только одной переменной ведомой и вспомогательной систем

Method for detection of characteristic phases of behavior in the intermittent generalized synchronization regime based on the use of an auxiliary system is considered. It is found that for the correct determination of the type of intermittency realized in the system, it is sufficient to use the only one variable characterizing the state of this system.

Особенности обобщенной синхронизации в системах с запаздыванием

Peculiarities of the generalized synchronization regime in unidirectionally coupled time-delayed generators are studied. Four different cases of interaction between systems characterized by different number of positive Lyapunov exponents are considered. The thresholds of the generalized synchronization regime onset is found to depend sufficiently on the degree of chaotic states of interacting systems, whereas the coupling between systems characterized by different number of positive Lyapunov exponents results in appearance of additional synchronous fields.

A method of distinguishing between the characteristic phases of behavior in complex networks in the intermittent generalized synchronization regime

A method of identification of the phases of synchronous and asynchronous intervals in the time realizations of interacting chaotic systems representing elements of a network with complex coupling topology in the state of transition to the generalized synchronization regime is proposed. The method allows determining the duration of the phases of synchronous and asynchronous dynamics, which potentially allows analyzing the statistical characteristics of the intermittent behavior of the discussed systems.

Binary generalized synchronization

In this paper we report for the first time on the binary generalized synchronization, when for the certain values of the coupling strength two unidirectionally coupled dynamical systems generating the aperiodic binary sequences are in the generalized synchronization regime. The presence of the binary generalized synchronization has been revealed with the help of both the auxiliary system approach and the largest conditional Lyapunov exponent calculation. The mechanism resulting in the binary generalized synchronization has been explained. The finding discussed in this paper gives a strong potential for new applications under many relevant circumstances.

Generalized synchronization in discrete maps. New point of view on weak and strong synchronization

In the present Letter we show that the concept of the generalized synchronization regime in discrete maps needs refining in the same way as it has been done for the flow systems Koronovskii et al. [Koronovskii AA, Moskalenko OI, Hramov AE. Nearest neighbors, phase tubes, and generalized synchronization. Phys Rev E 2011;84:037201]. We have shown that, in the general case, when the relationship between state vectors of the interacting chaotic maps are considered, the prehistory must be taken into account. We extend the phase tube approach to the systems with a discrete time coupled both unidirectionally and mutually and analyze the essence of the generalized synchronization by means of this technique. Obtained results show that the division of the generalized synchronization into the weak and the strong ones also must be reconsidered. Unidirectionally coupled logistic maps and Hénon maps coupled mutually are used as sample systems.

Generalized synchronization in mutually coupled oscillators and complex networks

We introduce a concept of generalized synchronization, able to encompass the setting of collective synchronized behavior for mutually coupled systems and networking systems featuring complex topologies in their connections. The onset of the synchronous regime is confirmed by the dependence of the system's Lyapunov exponents on the coupling parameter. The presence of a generalized synchronization regime is verified by means of the nearest neighbor method.

Nearest neighbors, phase tubes, and generalized synchronization

In this paper we report on the necessity of the refinement of the concept of generalized chaotic synchronization. We show that the state vectors of the interacting chaotic systems being in the generalized synchronization regime are related to each other by the functional, but not the functional relation as it was assumed until now. We propose the phase tube approach explaining the essence of generalized synchronization and allowing the detection and the study of this regime in many relevant physical circumstances. The finding discussed in this Brief Report provides great potential for different applications.

Effect of noise on generalized synchronization of chaos: theory and experiment

The influence of noise on the generalized synchronization regime in the chaotic systems with dissipative coupling is considered. If attractors of the drive and response systems have an infinitely large basin of attraction, generalized synchronization is shown to possess a great stability with respect to noise. The reasons of the revealed particularity are explained by means of the modified system approach [A.E. Hramov, A.A. Koronovskii, Phys. Rev. E 71, 067201 (2005)] and confirmed by the results of numerical calculations and experimental studies. The main results are illustrated using the examples of unidirectionally coupled chaotic oscillators and discrete maps as well as spatially extended dynamical systems. Different types of the model noise are analyzed. Possible applications of the revealed particularity are briefly discussed.

Experimental study of the generalized synchronization of chaotic oscillations in the presence of noise

The influence of an external source of noise on the position of the boundary of generalized synchronization (GS) of two unidirectionally coupled chaotic oscillators has been experimentally studied for the first time. It is established that the GS threshold remains unchanged in a broad range of the external noise intensity, i.e., the GS regime is stable with respect to external noise.

First Experimental Observation of Generalized Synchronization Phenomena in Microwave Oscillators

In this Letter, we report for the first time on the experimental observation of the generalized synchronization regime in the microwave electronic systems, namely, in the multicavity klystron generators. A new approach devoted to the generalized synchronization detection has been developed. The experimental observations are in the excellent agreement with the results of numerical simulation. The observed phenomena gives a strong potential for new applications requiring microwave chaotic signals.

Generalized chaotic synchronization in coupled Ginzburg-Landau equations

Generalized synchronization is analyzed in unidirectionally coupled oscillatory systems exhibiting spatiotemporal chaotic behavior described by Ginzburg-Landau equations. Several types of coupling between the systems are analyzed. The largest spatial Lyapunov exponent is proposed as a new characteristic of the state of a distributed system, and its calculation is described for a distributed oscillatory system. Partial generalized synchronization is introduced as a new type of chaotic synchronization in spatially nonuniform distributed systems. The physical mechanisms responsible for the onset of generalized chaotic synchronization in spatially distributed oscillatory systems are elucidated. It is shown that the onset of generalized chaotic synchronization is described by a modified Ginzburg-Landau equation with additional dissipation irrespective of the type of coupling. The effect of noise on the onset of a generalized synchronization regime in coupled distributed systems is analyzed.

Chaotic synchronization in coupled spatially extended beam–plasma systems

The appearance of the chaotic synchronization regimes has been discovered for the coupled spatially extended beam–plasma Pierce systems. The coupling was introduced only on the right bound of each subsystem. It has been shown that with coupling increase the spatially extended beam–plasma systems show the transition from asynchronous behavior to the phase synchronization and then to the complete synchronization regime. For the consideration of the chaotic synchronization we used the concept of time-scale synchronization described in work [A.E. Hramov, A.A. Koronovskii, Chaos 14 (3) (2004) 603] and based on the introduction of the continuous set of phases of chaotic signal. In case of unidirectional coupling the generalized synchronization regime has been observed in the spatially extended beam–plasma systems. The generalized synchronization appearance mechanism has been analyzed by means of the offered modified system approach [A.E. Hramov, A.A. Koronovskii, Phys. Rev. E 71 (6) (2005) 067201].

Generalized synchronization of chaotic oscillators

The behavior of two unidirectionally coupled chaotic oscillators near the boundary of their generalized synchronization is analyzed. Using the modified system method, the position of this boundary on the plane of control parameters is considered and the physical mechanisms leading to the establishment of the generalized synchronization regime are elucidated.

Generalized synchronization in coupled Ginzburg-Landau equations and mechanisms of its arising

Generalized chaotic synchronization regime is observed in the unidirectionally coupled one-dimensional Ginzburg-Landau equations. The mechanism resulting in the generalized synchronization regime arising in the coupled spatially extended chaotic systems demonstrating spatiotemporal chaotic oscillations has been described. The cause of the generalized synchronization occurrence is studied with the help of the modified Ginzburg-Landau equation with additional dissipation.

Generalized synchronization: A modified system approach

The universal mechanism resulting in the generalized synchronization regime arising in the chaotic oscillators with the dissipative coupling has been described. The reasons for the generalized synchronization occurrence may be clarified by means of a modified system approach. The main results are illustrated by unidirectionally coupled Rössler systems, Rössler and Lorenz systems, and logistic maps.