Function projective synchronization of different chaotic systems with uncertain parameters

This Letter investigates the function projective synchronization of different chaotic systems with unknown parameters. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the states of two different chaotic systems asymptotically synchronized up to a desired scaling function. Numerical simulations on Lorenz system and Newton-Leipnik system are presented to verify the effectiveness of the proposed scheme.     

Impulsive control of projective synchronization in chaotic systems

Scaling factor of projective synchronization in coupled partially linear chaotic systems is hardly predictable. To control projective synchronization of chaotic systems in a preferred way, an impulsive control scheme is introduced to direct the scaling factor onto a desired value. The control approach is derived from the impulsive differential equation theory. Numerical simulations on the chaotic Lorenz system are illustrated to verify the theoretical results. Furthermore, some interesting and surprising numerical results are discussed.     

High precision fast projective synchronization in chaotic (hyperchaotic) systems

A high precision fast projective synchronization method was proposed through introducing an impact factor. The numerical simulations indicate that the synchronization precision was increased three orders of magnitude higher than available methods in literature, under the same conditions of numerical method and hardware. The synchronization can achieved after first iteration. The synchronization speed has been increased by 13 484 times and 23 000 times when and , respectively, compared to general methods.     

Chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity

In this Letter, the concept of practical synchronization is introduced and the chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity is investigated. Based on the time-domain approach, a tracking control is proposed to realize chaos synchronization for the uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity. Moreover, the guaranteed exponential convergence rate and convergence radius can be pre-specified. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained result.     

Adaptive function projective synchronization of two-cell Quantum-CNN chaotic oscillators with uncertain parameters

This work investigates function projective synchronization of two-cell Quantum-CNN chaotic oscillators using adaptive method. Quantum-CNN oscillators produce nano scale chaotic oscillations under certain conditions. By Lyapunove stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.     

Switching phenomenon induced by breakdown of chaotic phase synchronization

We investigate chaotic phase synchronization (CPS) in three-coupled chaotic oscillator systems. According to the coupling strength and mismatches in the frequencies of these oscillators, we can observe complete CPS where all three oscillators exhibit CPS, and partial CPS where only two oscillators exhibit CPS. When the coupling strength is weakened, we observe a phenomenon that complete CPS among the three oscillators is suddenly disrupted without going through partial CPS. In this case oscillators exhibit quasi-CPS where two oscillators appear to exhibit CPS transiently, and the combination of the two oscillators changes with time. We call this phenomenon CPS switching D. It is revealed that phase fluctuation plays an important role in CPS switching D. It is also shown that the amplitude with a specific structure strengthens the degree of CPS switching. In the present paper, we characterize this CPS switching and discuss its mechanism.     

Projective synchronization of a class of delayed chaotic systems via impulsive control

The Letter studies the projective synchronization of a class of delayed chaotic systems. The drive-response system can be synchronized to within a desired scaling factor via impulsive control. Some sufficient conditions are derived by the stability analysis of the impulsive functional differential equations. An illustrative example is provided to show the effectiveness and feasibility of the proposed method and results.     

General methods for modified projective synchronization of hyperchaotic systems with known or unknown parameters

This work is concerned with the general methods for modified projective synchronization of hyperchaotic systems. A systematic method of active control is developed to synchronize two hyperchaotic systems with known parameters. Moreover, by combining the adaptive control and linear feedback methods, general sufficient conditions for the modified projective synchronization of identical or different chaotic systems with fully unknown or partially unknown parameters are presented. Meanwhile, the speed of parameters identification can be regulated by adjusting adaptive gain matrix. Numerical simulations verify the effectiveness of the proposed methods.     

Stochastic synchronization of coupled neural networks with intermittent control

In this Letter, we study the exponential stochastic synchronization problem for coupled neural networks with stochastic noise perturbations. Based on Lyapunov stability theory, inequality techniques, the properties of Weiner process, and adding different intermittent controllers, several sufficient conditions are obtained to ensure exponential stochastic synchronization of coupled neural networks with or without coupling delays under stochastic perturbations. These stochastic synchronization criteria are expressed in terms of several lower-dimensional linear matrix inequalities (LMIs) and can be easily verified. Moreover, the results of this Letter are applicable to both directed and undirected weighted networks. A numerical example and its simulations are offered to show the effectiveness of our new results.     

Parameter estimation using balanced synchronization

Synchronization between experimental observations and a dynamical model with undetermined parameters can assist in completing the specification of the model parameters. The quality of the synchronization, a cost function to be minimized, typically depends on the difference between the data time series and the model time series. If the coupling between the data and the model is too strong, this cost function is small for any data and any model, and the variation of the cost function with respect to the parameters of interest is too small to permit selection of a value of the parameters. If the coupling is too small, synchronization is lost. We introduce two methods for balancing the competing desires of a small cost function and the numerical ability to determine parameters accurately. One method of ‘balanced’ synchronization adds a requirement that the conditional Lyapunov exponent of the model system, conditioned on being driven by the data, remain negative but small. The other method allows the coupling to vary in time according to the error in synchronization. This second method succeeds because the data and the model exhibit generalized synchronization in the region where the parameters of the model are well determined.     

Function projective synchronization of two-cell quantum-CNN chaotic oscillators by nonlinear adaptive controller

In this Letter, we investigate function projective synchronization of two-cell quantum-CNN chaotic oscillators using nonlinear adaptive controller. Based on Lyapunov stability theory, the nonlinear adaptive control law is derived to make the state of two chaotic systems function projective synchronized. Two numerical simulations are presented to illustrate the effectiveness of the proposed nonlinear adaptive control scheme, which is more effective than that in previous literature.     

The chaotic phase synchronization in adaptively coupled-delayed complex networks

The notion of chaotic phase synchronization (CPS) in the large-scale delayed scale-free network is discussed in this Letter. The amplitude death (AD) phenomenon is observed and analyzed in terms of energy. AD occurs when the time-delay becomes long enough. The adaptive coupling scheme has better performance in CPS and AD compared with the constant scheme, and simulation results confirm conclusions.     

Conditions for common-noise-induced synchronization in time-delay systems

We studied synchronization induced by a common external noise in scalar time-delay systems. We have found a set of sufficient conditions for the synchronization. This set of conditions shows that the synchronization occurs in a wide class of time-delay systems. Numerical evidence for the analytically obtained conditions is also presented.     

Adaptive-impulsive synchronization in drive-response networks of continuous systems and its application

Based on the comparison theorem for the stability of impulsive control system, adaptive-impulsive synchronization in drive-response networks of continuous systems with time-delay and non-time-delay is investigated. And the continuous control input, the simple updated laws and a linear impulsive controller are proposed. Moreover, two numerical examples are presented to verify the effectiveness and correctness of the theorem, using the energy resource system and Lü's system as the nodes of the networks.     

Control-oriented approaches to anticipating synchronization of chaotic deterministic ratchets

In virtue of techniques derived from nonlinear control system theory, we establish conditions under which one could obtain anticipating synchronization between two periodically driven deterministic ratchets that are able to exhibit directed transport with a finite velocity. Criteria are established in order to guarantee the anticipating synchronization property of such systems as well as characterize phase space dynamics of the ratchet transporting behaviors. These results allow one to predict the chaotic direct transport features of particles on a ratchet potential using a copy of the same system that performs as a slave, which are verified through numerical simulation.     

Adiabatic small noise fluctuations around anticipated synchronization: A perspective from scalar master-slave dynamics

In this paper we extract and highlight some essential ingredients and properties that characterize the phenomenon of anticipated synchronization when external additive noise sources perturb the master and slave dynamics. Our results rely on a minimal scalar setup able to exhibit the more fundamental aspects of this phenomenon, where the fluctuations around the average dynamics are worked out in a small noise and adiabatic approximations allowing to describe their dynamics through linear delay Langevin equations. In this context, we find necessary conditions that guarantee anticipated synchronization in the mean value. Fluctuations around this condition are studied through the stationary correlation of the delayed difference between the master and slave dynamics. It is shown that external noise properties can be inferred by measuring this object. Conditions for minimizing the dynamical fluctuations around the anticipated synchronization in mean value are found. A detailed analysis of the dependence on the characteristic parameters is presented.     

Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays

In this Letter, we have dealt with the problem of lag synchronization and parameter identification for a class of chaotic neural networks with stochastic perturbation, which involve both the discrete and distributed time-varying delays. By the adaptive feedback technique, several sufficient conditions have been derived to ensure the synchronization of stochastic chaotic neural networks. Moreover, all the connection weight matrices can be estimated while the lag synchronization is achieved in mean square at the same time. The corresponding simulation results are given to show the effectiveness of the proposed method.     

Adaptive modified function projective synchronization between hyperchaotic Lorenz system and hyperchaotic Lu system with uncertain parameters

This Letter investigates modified function projective synchronization between hyperchaotic Lorenz system and hyperchaotic Lu system using adaptive method. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two hyperchaotic systems modified function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.     

Adaptive cluster synchronization in complex dynamical networks

Cluster synchronization is investigated in different complex dynamical networks. In this Letter, a novel adaptive strategy is proposed to make a complex dynamical network achieve cluster synchronization, where the adaptive strategy of one edge is adjusted only according to its local information. A sufficient condition about the global stability arbitrarily grouped of cluster synchronization is derived. Several numerical simulations show the effectiveness of the adaptive strategy.     

Spatiotemporal patterns and chaotic burst synchronization in a small-world neuronal network

The spatiotemporal patterns and chaotic burst synchronization of a small-world neuronal network are studied in this paper. The synchronization parameter, similarity parameter and order parameter are introduced to investigate the dynamics behaviour of the neurons. Chaotic burst synchronization and nearly complete synchronization can be observed if the link probability and the coupling strength are large enough. It is found that with increasing link probability and the coupling strength chaotic bursts become appreciably synchronous in space and coherent in time, and the maximal spatiotemporal order appears at some particular values of the probability and the coupling strength, respectively. The larger the size of the network, the smaller the probability and the coupling strength are needed for the network to achieve burst synchronization. Moreover, the bursting activity and the spatiotemporal patterns are robust to small noise.