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Investigating the stability of the synchronization manifold is a critical topic in the field of complex dynamical networks. Master stability function (MSF) is known as a powerful and efficient tool for the study of synchronization in complex identical networks. The network can be synchronized whenever the MSF is negative. MSF uses the Lyapunov or Floquet exponent theory to determine the stability of the synchronization state. Both of these methods need extensive numerical simulation and a long computational time. In this paper, a new approach to calculate MSF is proposed. The accuracy of the results and time of simulations are tested on seven different known oscillators and also compared with the conventional methods of MSF. The results show that the proposed technique is faster and more efficient than the existing methods. [ABSTRACT FROM AUTHOR]

In this paper, based on the idea of nonlinear observer, lag synchronization of chaotic fractional system with commensurate and incommensurate order is studied by the stability theorem of linear fractional-order systems. The theoretical analysis of fractional-order systems in this paper is a systematic method. This technique is applied to achieve the lag synchronization of fractional-order Rössler's system, verified by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper studies the synchronizability of power network with community structure. Second-order Kuramoto-like oscillators with dissimilar natural frequencies are used as a coarse-scale model for an electrical power network that contains generators and consumers. The impact of community structure on frequency synchronization of power network is investigated, focusing on the parameters such as community strength, community number and connection strategy between communities. Numerical simulations show that increasing the community strength above a certain critical threshold or adding new communities to the network will be beneficial for the synchronization. Of course, connecting high-degree nodes among communities will be a best strategy to enhance synchronization. Furthermore, it is observed that the synchronizability of the network is significantly influenced by adding new links with different characteristics. [ABSTRACT FROM AUTHOR]

In this paper, based on Lyapunov stability theory, a novel scheme is proposed to explore the lag synchronization of Coullet system. Via back stepping method, the scheme needs only a single controller and the sufficient condition of synchronization is derived. To illustrate the effectiveness of the proposed scheme, some numerical simulations are presented. [ABSTRACT FROM AUTHOR]

In this paper, a chaotic synchronization scheme is proposed to achieve adaptive synchronization between a novel hyperchaotic system and the hyperchaotic Chen system with fully unknown parameters. Based on the Lyapunov stability theory, an adaptive controller and parameter updating law are presented to synchronize the above two hyperchaotic systems. The corresponding theoretical proof is given and numerical simulations are presented to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, a chaotic synchronization scheme is proposed to achieve the generalized synchronization between two different fractional-order chaotic systems. Based on the stability theory of fractional-order systems and the pole placement technique, a controller is designed and theoretical proof is given. Two groups of examples are shown to verify the effectiveness of the proposed scheme, the first one is to realize the generalized synchronization between the fractional-order Chen system and the fractional-order Rössler system, the second one is between the fractional-order Lü system and the fractional-order hyperchaotic Lorenz system. The corresponding numerical simulations verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper presents the general method for the adaptive function Q-S synchronization of different chaotic (hyper-chaotic) systems. Based upon the Lyapunov stability theory, the dynamical evolution can be achieved by the Q-S synchronization with a desired scaling function between the different chaotic (hyper-chaotic) systems. This approach is successfully applied to two examples: Chen hyper-chaotic system drives the Lorenz hyper-chaotic system; Lorenz system drives Lü hyper-chaotic system. Numerical simulations are used to validate and demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time chaos synchronization of a new hyperchaotic Lorenz system. Based on the finite-time stability theory, a simple and robust controller is proposed to realize finite-time chaos synchronization for the hyperchaotic Lorenz system. Theoretical analysis proved that the scheme can ensure the error system globally finite-time stable. Numerical simulations are provided to show the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

Projective synchronization investigates the synchronization of systems evolve in same orientation, however, in practice, the situation of same orientation is only minority, and the majority is different orientation. This paper investigates the latter, proposes the concept of rotating synchronization, and verifies its necessity and feasibility via theoretical analysis and numerical simulations. Three conclusions were elicited: first, in three-dimensional space, two arbitrary nonlinear chaotic systems who evolve in different orientation can realize synchronization at end; second, projective synchronization is a special case of rotating synchronization, so, the application fields of rotating synchronization is more broadly than that of the former; third, the overall evolving information can be reflected by single state variable's evolving, it has self-similarity, this is the same as the basic idea of phase space reconstruction method, it indicates that we got the same result from different approach, so, our method and the phase space reconstruction method are verified each other. [ABSTRACT FROM AUTHOR]

In this paper, a generalized (lag, anticipated and complete) projective synchronization for a general class of chaotic systems is defined. A systematic, powerful and concrete scheme is developed to investigate the generalized (lag, anticipated and complete) projective synchronization between the drive system and response system based on the adaptive control method and feedback control approach. The hyperchaotic Chen system and hyperchaotic Lorenz system are chosen to illustrate the proposed scheme. Numerical simulations are provided to show the effectiveness of the proposed schemes. In addition, the scheme can also be extended to research generalized (lag, anticipated and complete) projective synchronization between nonidentical discrete-time chaotic systems. [ABSTRACT FROM AUTHOR]

This paper analyzes the synchronizations for autonomous chaotic systems with disturbance of parameter, achieves the self-synchronization of Lü system, a modified coupled dynamos system and a four-dimensional hyperchaotic system by the methods of active control and adaptive parameter. In addition, the synchronization of Lorenz system and Chen system is presented. Numerical simulations are provided for illustration and verification of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies full state hybrid projective synchronization of the unified chaotic system with unknown parameters. Based on the Lyapunov stability theory, an adaptive controller is designed. It is proved theoretically that the controller can make the states of the dynamical system and the response system with unknown parameters asymptotically full state hybrid projective synchronized. Numerical simulations show the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

The impulsive synchronization of two chaotic Chen-Lee systems was investigated in this paper. Based on Lyapunov's direct method, sufficient conditions for the global exponential synchronization and global asymptotical synchronization were derived. Further, the theoretical results were verified by a numerical simulation. In addition, the impulsive synchronization of two chaotic Chen-Lee systems was also implemented using an electronic circuit. [ABSTRACT FROM AUTHOR]

This paper presents tracking control and synchronization strategies for Chen system. Two universal controllers, a tracking controller and a synchronization controller based on Backstepping design method were designed. It is proved theoretically that the tracking controller enables the error signal exponentially to converge to zero. The validity of Backstepping synchronization controller is also proved. Numerical simulations further validated the two controllers. [ABSTRACT FROM AUTHOR]

In this paper, the impulsive synchronization of hyperchaotic Lü systems is discussed. The sufficient conditions on feedback strength and impulsive interval are established to guarantee the synchronization. The method is proved true by Lyapunov stability theory. In addition, a scheme of impulsive synchronization via transmitting single signal is presented. Numerical simulations show the effectiveness of the methods. [ABSTRACT FROM AUTHOR]

In this paper, the drive system and the response system can be in a state of linear generalized synchronization via transmitting single signal. By means of a transitional system, the response system is obtained by variable replacement method. Chen system and hyperchaotic Chen system are used as examples in numerical simulations. Simulation results show the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Synchronization of multiple identical chaotic systems, coupled in a ring structure, was studied in this paper. Ueda attractor was used as an example to perform the synchronization of several chaotic systems. The bound of the Ueda attractor was also estimated by numerical simulation. The above results were also adopted to design a controller to synchronize chaotic systems. The stability of the synchronization of multiple identical chaotic systems was investigated using Lyapunov's direct method. Some sufficient conditions of asymptotical synchronization were attained from rigorous mathematical theory. Further, numerical results were also demonstrated in order to validate the proposed synchronization approach. [ABSTRACT FROM AUTHOR]

oActive sliding mode control is one of the effective methods to synchronize chaotic systems in the presence of uncertainties. Use of the method, however, requires decision making on how to choose the control parameters for a specific performance. In this paper we propose an algorithm to determine the best control parameters for which the minimum control efforts are required to synchronize two identical or non-identical chaotic systems. We have also determined the maximum range of the uncertainties on which the selected control parameters to work properly. The effectiveness of the proposed method has been verified through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates antisynchronization of identical and nonidentical Φ6 Van der Pol oscillators (VDPOs) and Φ6 Duffing oscillators (DOs) with both parametric and external excitations based on adaptive backstepping technique. The technique is applied to achieve complete antisynchronization between identical Φ6 (VDPOs), identical Φ6 (DOs), and nonidentical Φ6 oscillators comprising the Φ6 (VDPO) and Φ6 (DO). Numerical simulations are implemented to verify the feasibility and effectiveness of the antisynchronization technique. [ABSTRACT FROM AUTHOR]

In the paper, generalized chaotic synchronization of a class of fractional order systems is studied. Based on the stability theory of linear fractional order systems, a generalized synchronization scheme is presented, and theoretical analysis is provided to verify its feasibility. The proposed method can realize generalized synchronization not only of fractional order systems with same dimension, but also of systems with different dimensions. Besides, the function relation of generalized synchronization can be linear or nonlinear. Numerical simulations show the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

This paper investigates chaotic synchronization in the generalized sense in two resistive-capacitive-inductive-shunted (RCL-shunted) Josephson junctions (RCLSJJs) by using the means of unidirectionally coupling. The numerical simulations confirm that the generalized synchronization of chaos in these two systems can be achieved with a suitable coupling intensity when the maximum condition Lyapunov exponent (MCLE) is negative. Also, the auxiliary system approach is used to detect the existence of the generalized synchronization. [ABSTRACT FROM AUTHOR]

This paper studies a type of single scroll attractor chaos system. Based on the research of Jiang et al. the global synchronization method is designed, and moreover, the author uses a combined synchronization of linear and nonlinear feedback, active control, single vector and unidirectional coupling synchronization three methods else, the problem of synchronization between same and different chaotic systems are realized by the four methods, respectively. The range of control function parameter is discussed according to the Routh-Hurwitz criterion and numerical simulations show the effectiveness of them. [ABSTRACT FROM AUTHOR]

Assuming the Rössler system as a reference, this paper studies two cases of chaotic synchronization of a pair of (master and slave) systems: one with fully uncertain parameters for both, the other where the master system has fixed given parameters while the slave system is endowed with uncertain parameters. The respective adaptive controller based on parameter identification is then designed, according to the Lyapunov stability theorem. Then, it is proved that the two controllers are capable of making the two (identical) Rössler systems asymptotically synchronized. Numerical simulation results further testify the efficiency of controllers. [ABSTRACT FROM AUTHOR]

This paper addresses the adaptive synchronization problem of a class of different uncertain chaotic systems. A general adaptive robust controller and parameters update rule are designed. It is proved theoretically that the controller and update rule can make the drive-response systems with different structures asymptotically synchronized, and change the unknown parameters to constants when noise exists. When the drive system is certain, the unknown parameters of the response system can be updated to the predicted values. The results of numerical simulations show the effectiveness of the adaptive controller. [ABSTRACT FROM AUTHOR]