Robust H_∞ cluster synchronization analysis of Lurie dynamical networks

The cluster synchronization problem of complex dynamical networks with each node being a Lurie system with exter- nal disturbances and time-varying delay is investigated in this paper. Some criteria for cluster synchronization with desired H∞ performance are presented by using a local linear control scheme. Firstly, sufficient conditions are established to realize cluster synchronization of the Lurie dynamical networks without time delay. Then, the notion of the cluster synchronized region is introduced, and some conditions guaranteeing the cluster synchronized region and unbounded cluster synchro- nized region are derived. Furthermore, the cluster synchronization and cluster synchronized region in the Lurie dynamical networks with time-varying delay are considered. Numerical examples are finally provided to verify and illustrate the theoretical results.     

Robust H_∞ observer-based control for synchronization of a class of complex dynamical networks

This paper is concerned with the robust H∞ synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities (LMIs). The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.     

Mixed H_∞ and Passive Projective Synchronization for Fractional Order Memristor-Based Neural Networks with Time-Delay and Parameter Uncertainty

This paper investigates the mixed H∞ and passive projective synchronization problem for fractional-order(FO) memristor-based neural networks. Our aim is to design a controller such that, though the unavoidable phenomena of time-delay and parameter uncertainty are fully considered, the resulting closed-loop system is asymptotically stable with a mixed H∞ and passive performance level. By combining active and adaptive control methods, a novel hybrid control strategy is designed, which can guarantee the robust stability of the closed-loop system and also ensure a mixed H∞ and passive performance level. Via the application of FO Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequality techniques. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.     

Robust H∞ observer-based of a class of complex control for synchronization dynamical networks

This paper is concerned with the robust Hoo synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities （LMIs）. The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.     

Complete and phase synchronization in a heterogeneous small-world neuronal network

Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh--Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.     

Cost and effect of pinning control for network synchronization

The problem of pinning control for the synchronization of complex dynamical networks is discussed in this paper. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that a lower cost is achieved by using the control scheme of pinning nodes with smaller degrees. Some strict mathematical analyses are presented for achieving a lower cost in the synchronization of different star-shaped networks. Numerical simulations on some non-regular complex networks generated by the Barabási--Albert model and various star-shaped networks are performed for verification and illustration.     

H_∞ synchronization of chaotic Hopfield networks with time-varying delay: a resilient DOF control approach

This paper focuses on the issue of resilient dynamic output-feedback(DOF) control for H_∞ synchronization of chaotic Hopfield networks with time-varying delay. The aim is to determine a DOF controller with gain perturbations ensuring that the H_∞ norm from the external disturbances to the synchronization error is less than or equal to a prescribed bound. A delaydependent criterion for the H_∞ synchronization is derived by employing the Lyapunov functional method together with some recent inequalities. Then, with the help of some decoupling techniques, sufficient conditions on the existence of the resilient DOF controller are developed for both the time-varying and constant time-delay cases. Lastly, an example is used to illustrate the applicability of the results obtained.     

Robust fault-sensitive synchronization of a class of nonlinear systems

Aiming at enhancing the quality as well as the reliability of synchronization,this paper is concerned with the fault detection issue within the synchronization process for a class of nonlinear systems in the existence of external disturbances.To handle such problems,the concept of robust fault-sensitive (RFS) synchronization is proposed,and a method of determining such a kind of synchronization is developed.Under the framework of RFS synchronization,the master and the slave systems are robustly synchronized,and at the same time,sensitive to possible faults based on a mixed H /H ∞ performance.The design of desired output feedback controller is realized by solving a linear matrix inequality,and the fault sensitivity H index can be optimized via a convex optimization algorithm.A master-slave configuration composed of identical Chua’s circuits is adopted as a numerical example to demonstrate the effectiveness and applicability of the analytical results.     

Global Synchronization of Directed Networks with Fast Switching Topologies

Global synchronization of a class of directed dynamical networks with switching topologies is investigated. It is found that if there is a directed spanning tree in the fixed time-average of network topology and the time-average is achieved sufficiently fast, then the network will reach global synchronization for sufficiently large coupling strength.     

Pinning synchronization of time-varying delay coupled complex networks with time-varying delayed dynamical nodes

This paper deals with the pinning synchronization of nonlinearly coupled complex networks with time-varying coupling delays and time-varying delays in the dynamical nodes.We control a part of the nodes of the complex networks by using adaptive feedback controllers and adjusting the time-varying coupling strengths.Based on the Lyapunov-Krasovskii stability theory for functional differential equations and a linear matrix inequality(LMI),some sufficient conditions for the synchronization are derived.A numerical simulation example is also provided to verify the correctness and the effectiveness of the proposed scheme.     

Robust adaptive synchronization of uncertain and delayed dynamical complex networks with faulty network

<正>This paper presents a new robust adaptive synchronization method for a class of uncertain dynamical complex networks with network failures and coupling time-varying delays.Adaptive schemes are proposed to adjust controller parameters for the faulty network compensations,as well as to estimate the upper and lower bounds of delayed state errors and perturbations to compensate the effects of delay and perturbation on-line without assuming symmetry or irreducibility of networks.It is shown that,through Lyapunov stability theory,distributed adaptive controllers constructed by the adaptive schemes are successful in ensuring the achievement of asymptotic synchronization of networks in the present of faulty and delayed networks,and perturbation inputs.A Chua's circuit network example is finally given to show the effectiveness of the proposed synchronization criteria.     

Comparison of Phase Synchronizability of Several Regular Networks for Non-Phase-Coherent Attractors

Though applying master stability function method to analyse network complete synchronization has been well studied in chaotic dynamical systems, it does not work well for phase synchronization. Moreover, it is difficult to identify phase synchronization with the angle of rotation for non-phase-coherent attractors. We employ the recurrences plot method to detect phase synchronization for several regular networks with non-phase-coherent attractors. It is found that the coupling strength μ is different for different coupled networks. The coupling strength μ is reduced as completed coupled network scale enlarges, the coupling strength μ of star coupled network is irrelevant to network scale, and these two regular networks are easier to achieve phase synchronization. However, for ring and chain coupled networks, the larger the phase synchronization couple strength μ is, the larger the network scale is, and it is more difficult to achieve phase synchronization. For same scale network, once ring coupled structure becomes a chain coupled structure, phase synchronization becomes much more difficult.     

Adaptive synchronization in an array of asymmetric coupled neural networks

This paper investigates the global synchronization in an array of linearly coupled neural networks with constant and delayed coupling. By a simple combination of adaptive control and linear feedback with the updated laws, some sufficient conditions are derived for global synchronization of the coupled neural networks. The coupling configuration matrix is assumed to be asymmetric, which is more coincident with the realistic network. It is shown that the approaches developed here extend and improve the earlier works. Finally, numerical simulations are presented to demonstrate the effectiveness of the theoretical results.     

Adaptive Synchronization between Two Different Complex Networks with Time-Varying Delay Coupling

A new general network model for two complex networks with time-varying delay coupling is presented. Then we investigate its synchronization phenomena. The two complex networks of the model differ in dynamic nodes, the number of nodes and the coupling connections. By using adaptive controllers, a synchronization criterion is derived. Numerical examples are given to demonstrate the effectiveness of the obtained synchronization criterion. This study may widen the application range of synchronization, such as in chaotic secure communication.     

Nonlinear H∞ control of structured uncertain stochastic neural networks with discrete and distributed time varying delays

This paper is concerned with the problem of robust H∞ control for structured uncertain stochastic neural networks with both discrete and distributed time varying delays. A sufficient condition is presented for the existence of H∞ control based on the Lyapunov stability theory. The stability criterion is described in terms of linear matrix inequalities （LMIs）, which can be easily checked in practice. An example is provided to demonstrate the effectiveness of the proposed result.     

Small-World Connections to Induce Firing Activity and Phase Synchronization in Neural Networks

We investigate how the firing activity and the subsequent phase synchronization of neural networks with smallworld topological connections depend on the probability p of adding-links. Network elements are described by two-dimensional map neurons （2DMNs） in a quiescent original state. Neurons burst for a given coupling strength when the topological randomness p increases, which is absent in a regular-lattice neural network. The bursting activity becomes frequent and synchronization of neurons emerges as topological randomness further increases. The maximal firing frequency and phase synchronization appear at a particular value of p. However, if the randomness p further increases, the firing frequency decreases and synchronization is apparently destroyed.     

Random shortcuts induce phase synchronization in complex Chua systems

This paper studies how phase synchronization in complex networks depends on random shortcuts, using the piecewise-continuous chaotic Chua system as the nodes of the networks. It is found that for a given coupling strength, when the number of random shortcuts is greater than a threshold the phase synchronization is induced. Phase synchronization becomes evident and reaches its maximum as the number of random shortcuts is further increased. These phenomena imply that random shortcuts can induce and enhance the phase synchronization in complex Chua systems. Furthermore, the paper also investigates the effects of the coupling strength and it is found that stronger coupling makes it easier to obtain the complete phase synchronization.     

Generalized Projective Synchronization between Two Complex Networks with Time-Varying Coupling Delay

Generalized projective synchronization （GPS） between two complex networks with time-varying coupling delay is investigated. Based on the Lyapunov stability theory, a nonlinear controller and adaptive updated laws are designed. Feasibility of the proposed scheme is proven in theory. Moreover, two numerical examples are presented, using the energy resource system and Lü＇s system [Physica A 382 （2007） 672] as the nodes of the networks. GPS between two energy resource complex networks with time-varying coupling delay is achieved. This study can widen the application range of the generalized synchronization methods and will be instructive for the demand supply of energy resource in some regions of China.     

Linear-control-based synchronization of coexisting attractor networks with time delays

This paper introduces the concept of linear-control-based synchronization of coexisting attractor networks with time delays.Within the new framework,closed loop control for each dynamic node is realized through linear state feedback around its own arena in a decentralized way,where the feedback matrix is determined through consideration of the coordination of the node dynamics,the inner connected matrix and the outer connected matrix.Unlike previously existing results,the feedback gain matrix here is decoupled from the inner matrix;this not only guarantees the flexible choice of the gain matrix,but also leaves much space for inner matrix configuration.Synchronization of coexisting attractor networks with time delays is made possible in virtue of local interaction,which works in a distributed way between individual neighbours,and the linear feedback control for each node.Provided that the network is connected and balanced,synchronization will come true naturally,where theoretical proof is given via a Lyapunov function.For completeness,several illustrative examples are presented to further elucidate the novelty and efficacy of the proposed scheme.     

Linear-control-based synchronisation of coexisting attractor networks with time delays

This paper introduces the concept of linear-control-based synchronization of coexisting attractor networks with time delays. Within the new framework, closed loop control for each dynamic node is realized through linear state feedback around its own arena in a decentralized way, where the feedback matrix is determined through consideration of the coordination of the node dynamics, the inner connected matrix and the outer connected matrix. Unlike previously existing results, the feedback gain matrix here is decoupled from the inner matrix; this not only guarantees the flexible choice of the gain matrix, but also leaves much space for inner matrix configuration. Synchronization of coexisting attractor networks with time delays is made possible in virtue of local interaction, which works in a distributed way between individual neighbours, and the linear feedback control for each node. Provided that the network is connected and balanced, synchronization will come true naturally, where theoretical proof is given via a Lyapunov function. For completeness, several illustrative examples are presented to further elucidate the novelty and efficacy of the proposed scheme.