Coupled Complex Dynamical Networks Research Articles

Pinning clustering component synchronization of nonlinearly coupled complex dynamical networks

<abstract><p>In this paper, the clustering component synchronization of nonlinearly coupled complex dynamical networks with nonidentical nodes was investigated. By applying feedback injections to those nodes who have connections with other clusters, some criteria for achieving clustering component synchronization were obtained. A numerical simulation was also included to verify the correctness of the results obtained.</p></abstract>

New finite-time synchronization conditions of delayed multinonidentical coupled complex dynamical networks.

In this article, we mainly focus on the finite-time synchronization of delayed multinonidentical coupled complex dynamical networks. By applying the Zero-point theorem, novel differential inequalities, and designing three novel controllers, we obtain three new criteria to assure the finite-time synchronization between the drive system and the response system. The inequalities occurred in this paper are absolutely different from those in other papers. And the controllers provided here are fully novel. We also illustrate the theoretical results through some examples.

Adaptively Synchronize the Derivative Coupled Complex Networks With Proportional Delay

This article investigates adaptive control and exponential synchronization of a kind of derivative coupled complex dynamical networks (CDNs) with proportional delay. Based on impulsive control and adaptive pinning control protocols, sufficient criteria for achieving of the exponential synchronization on CDNs are obtained by jointly applying the proportional delayed impulsive comparison principle, the extended parameters variation formula and the definition of average impulsive interval. Meanwhile, suitable control gains for achieving adaptive synchronization are acquired according to the efficiently designed adaptive updating laws. In addition, the convergence velocity of the exponential synchronization is precisely estimated. Finally, one numerical simulation is presented to illustrate the validity of the adaptive pinning control protocols and theoretical results. By introducing the concept of impulsive distance for the first time, the example further explains the dynamic balance between the impulsive effects and the feedback control gains, which provides a method in controller designing.

Fault estimation and synchronization control for complex dynamical networks with time‐varying coupling delay

AbstractThis article is devoted to simultaneously solve the problems of fault estimation and synchronization for a class of delayed coupling complex dynamical networks. First, an intermediate estimator is established for each node with the aid of the relative information from the neighboring nodes. Second, a distributed memory state feedback controller is designed with respect to the estimated state values and fault signals. Third, some error systems are formulated by introducing appropriate linear transformations. Then, a set of delay‐dependent criteria is obtained to ensure that the states of the resulting systems are uniformly bounded and subsequently, the explicit design method of the desired gain matrices is presented. At last, the feasibility of established theoretical results is validated by the support of two numerical examples in which one is an application example based on the aircraft model. Different from the existing fault estimation techniques, the proposed method does not require the observer matching condition and the upper bounds of the fault signals, which reduces the conservatism significantly.

Pinning synchronization for delayed coupling complex dynamical networks with incomplete transition rates Markovian jump

In this paper, the synchronization problem is investigated for a class of time-varying delayed coupling complex dynamical networks subject to incomplete transition rates Markovian switching typologies via pinning control scheme. Compared with most of previous relative networks, a more general network model is discussed and in which the transition rates in Markovian processes are uncertain or completely unknown. The complete knowledge on the transition rates is difficult to precisely acquire on account of the limitations of equipment and environmental impacts. Only a single feedback controller is utilized and, by constructing time dependent Lyapunov–Krasovskii functions, applying an extended Jensen’s integral inequality as well as some inequality techniques, some criteria are obtained for guaranteeing stochastic synchronization of considered networks. Moreover, similar results can be also presented for Markovian jump complex dynamical networks without time-varying delay. The obtained results improve and extend some existing relevant results. In the end, some simulation examples are provided to illustrate the effectiveness of the proposed method.

Adaptive Synchronization of Complex Dynamical Networks via Distributed Pinning Impulsive Control

In this paper, exponential synchronization of a class of nonlinearly coupled complex dynamical networks with time-varying delay is investigated. A novel distributed controller combined with pinning impulsive method is designed by selecting the systems with largest norms of errors to be controlled at every impulsive instant. By introducing the adaptive control protocol into the negative feedback controller, suitable control gains are obtained and therefore, the control cost is efficiently saved. Based on the Lyapunov stability theory and some mathematical techniques, some novel leader-following synchronization criteria are derived. Furthermore, with consideration of time-varying impulsive effects, the obtained results are extended to a more complicated situation. Finally, two numerical examples are performed to illustrate the effectiveness of the theoretical analysis.

Pinning Synchronization of Nonlinearly Coupled Complex Dynamical Networks on Time Scales

In this paper, we study the synchronization problem for nonlinearly coupled complex dynamical networks on time scales. To achieve synchronization for nonlinearly coupled complex dynamical networks on time scales, a pinning control strategy is designed. Some pinning synchronization criteria are established for nonlinearly coupled complex dynamical networks on time scales, which guarantee the whole network can be pinned to some desired state. The model investigated in this paper generalizes the continuous-time and discrete-time nonlinearly coupled complex dynamical networks to a unique and general framework. Moreover, two numerical examples are given for illustration and verification of the obtained results.

Robust synchronization in finite time for fractional-order hybrid coupling discontinuous complex dynamic networks with nonlinear growth

In this paper, the global robust synchronization and synchronization in finite time are considered for fractional-order hybrid coupling complex dynamical networks (CDNs), where the growth of dynamic nodes is discontinuous, and subjected to a quadratic polynomial. Firstly, a convergence principle in finite time is developed for fractional-order nonlinear systems with discontinuous right-hand side. Secondly, a suitable discontinuous controller without the terms of time delays is designed, and the global robust synchronization condition is addressed in the terms of linear matrix inequalities (LMIs) by applying Lyapunov functional approach, inequality analysis technique, and Clarke’s non-smooth analysis method. In addition, the global robust synchronization goal in finite time is achieved by utilizing the developed convergence principle. Moreover, the upper bound of the settling time for the global robust synchronization in finite time is explicitly evaluated. Finally, the feasibility of the proposed design scheme and the validity of theoretical results are verified by two numerical simulation examples.

Composite synchronization control for delayed coupling complex dynamical networks via a disturbance observer-based method

Based on state feedback control approach and disturbance observer method, a new composite synchronization control strategy is presented in this study for a class of delayed coupling complex dynamical networks with two different types of disturbances. Herein, one of the disturbances is produced by an exogenous system which acts through the input channel, while the other is usual norm-bounded. The main objective of this study is to exactly estimate the disturbance at the input channel, whose output is integrated with the state feedback control law. In this study, the composite control strategy is designed in two forms according to the present and past states’ information about the system. By applying the Lyapunov–Krasovskii stability theory, a new set of sufficient conditions is obtained for the existence of both control strategies separately through the feasible solution of a series of matrix inequalities. The superiority and validity of the developed theoretical results are demonstrated by two numerical examples, wherein it is shown that the proposed control strategy is capable of handling multiple disturbances in the synchronization analysis.

Function matrix projective synchronization of non-dissipatively coupled heterogeneous systems with different-dimensional nodes

This paper regards function matrix projective synchronization of two different non-dissipatively coupled complex dynamical networks for different dimensions and different nodes. In this kind of complex dynamical networks the internal delays are different from the coupled delays. By using Lyapunov stability theory, using mathematical induction, two different hybrid feedback controllers are built to realize the function matrix projective synchronization. Compared with the existing results, the coupling matrices do not need to be symmetric or diffuse. By giving a numerical simulation we explain the validity and appropriateness of our conclusion.

Global synchronization in finite time for fractional-order coupling complex dynamical networks with discontinuous dynamic nodes

The global Mittag–Leffler synchronization and global synchronization problem in finite time for fractional-order complex networks which with discontinuous nodes is studied in this paper. When the coupling matrix is time-varying and unknown, under the designed adaptive law with respect to the coupling matrix, by utilizing nonsmooth analysis method and Lyapunov functional approach as well as Laplace transform technique, the conditions of global Mittag–Leffler synchronization are achieved in terms of linear matrix inequalities (LMIs). When the coupling matrix is invariable and known, under the designed feedback controller, and by constructing a Lur’e Postnikov-type Lyapunov functional, the conditions of global synchronization in finite time are established, which are in the form of LMIs, and the upper bound of the settling time is explicitly evaluated. Finally, two examples are provided to illustrate the validity of the proposed design method and theoretical results.

State Estimation for Coupled Output Complex Dynamical Networks with Stochastic Sampled-Data

In this paper, the problem of the state estimation on complex dynamical networks coupled with stochastically sampling is studied. By using the input delay approach, the sampled-data system is transformed into a time-continuous system where the data at sampling periods have two different time-varying delays randomly happening between two intervals which have different known lower and upper bounds. The sampling points occur with two known probabilities and satisfy Bernoulli distribution. There are two different types of stochastically-sampled-data considered in this complex dynamical network. One of the stochastically-sampled-data is used to data exchange over the dynamical network, the other is used to construct the Luenburger state estimator as feedback data. We derive the state estimator for the complex dynamical network with new models which combined with two types of above stochastic-sampled-data, and delay-dependent asymptotical stabilities of the estimation error has been solved by constructing a Lyapunov–Krasovskii functional and the linear matrix inequality toolbox in MATLAB. Finally, a numerical example has been illustrated to demonstrate the effectiveness of the proposed results.

Model-Free Fault Tolerant Control for a Class of Complex Dynamical Networks With Derivative Couplings.

This paper studies the fault tolerant synchronization control for a class of derivative coupled complex dynamical networks (CDNs). Different from the existing results, each subsystem model is assumed to be completely unknown and the coupling terms are mismatched with the control input. Within this framework, a novel model-free fault tolerant controller is designed. Under the proposed control law, the synchronization errors of CDNs are proved to asymptotically converge to zero, which means that the synchronization is successfully achieved. Especially, by combining an important spectral decomposition technique and some properties of Laplacian matrix, a data-based algorithm is provided to derive the controller parameter. In addition, the proposed method is also valid for the CDNs with unknown coupling weights. Finally, examples on circuit systems are given to verify the theoretical results, and some circuit realizations of the proposed control law are implemented based on the circuit theory.

Secure communication scheme analysis via complex networks

SummaryRecently, some existing works have introduced novel way to construct complex networks from embedded time series, which provides new sights into the organizational properties of the time series in phase space. In this paper, we attempt to answer the fundamental question of “how much information regarding the dynamic property of the original time series can be extracted from these networks.” To this end, we propose a new method for reconstructing time series from the networks. We compare the reconstructed time series from these networks and that from the recurrence plot. We find that these networks contain topological information of the embedded time series to a certain degree. In general, they are more powerful than the recurrence plot method in the reconstruction of embedded time series. In addition, we study a new generalized projective synchronization (GPS) of coupled complex dynamical networks with different sizes via feedback control and impulsive control. Based on the stability analysis of impulsive system, a network synchronization criterion is established. These works may find potential application for secure communication via networks.

Generalized outer synchronization between non-dissipatively coupled complex networks with different-dimensional nodes

• Asymptotic and exponential generalized outer synchronization criteria are proposed. • Only partial dynamics of each node in the response network is constrained by QUAD. • Our network nodes may be non-dissipatively coupled and have different dimensions. • Our network models possess different time-varying coupling configurations. • Our networks have nonlinear inner functions and different time-varying delays. This paper investigates the generalized outer synchronization (GOS) between two non-dissipatively coupled complex dynamical networks (CDNs) with different time-varying coupling delays. Our drive-response networks also possess nonlinear inner coupling functions and time-varying outer coupling configuration matrices. Besides, in our network models, the nodes in the same network are nonidentical and the nodes in different networks have different state dimensions. Asymptotic generalized outer synchronization (AGOS) and exponential generalized outer synchronization (EGOS) are defined for our CDNs. Our main objective in this paper is to design AGOS and EGOS controllers for our drive-response networks via the open-plus-closed-loop control technique. Distinguished from most existing literatures, it is the partial intrinsic dynamics of each node in response network that is restricted by the QUAD condition, which is easy to be satisfied. Representative simulation examples are given to verify the effectiveness and feasibility of our GOS theoretical results in this paper.

Pinning cluster synchronization of delay-coupled Lur’e dynamical networks in a convex domain

This paper devotes to investigating the cluster synchronization of coupled complex dynamical networks consisted of Lur’e systems with time-varying delay. By considering the topology structure of the complex network, an effective pinning controller is designed which not only synchronize all Lur’e systems in the same cluster, but also decrease the influence among different clusters. Firstly, based on delay interval dividing methods, expended Jensen’s inequality and Jacobian methods, sufficient conditions for local cluster synchronization of the Lur’e dynamical networks are derived by applying the specially designed pinning controller. Secondly, the convex combination theorem, S-procedure and the definition of delay rate are jointly applied in order to obtain the delay-dependent stability criteria which guarantee the global cluster synchronization of the Lur’e networks under the pinning control strategy. And finally, some numerical simulations are given to illustrate the validity of the control scheme and the theoretical analysis.

Global Exponential Synchronization of Nonlinearly Coupled Complex Dynamical Networks with Time-Varying Coupling Delays

This paper focuses on the global exponential synchronization problem of nonlinearly coupled complex dynamical networks with time-varying coupling delays. Several simple and generic global exponential synchronization criteria are derived based on the Lyapunov stability theory and the Dini derivatives using the Halanay and generalized Halanay inequalities. These criteria rely on system parameters alone and can be used conveniently in practical applications. In addition, the system parameters do not satisfy the conditions of the proposed criteria. That is, the system itself cannot synchronize. However, system synchronization can be achieved by adding the appropriate feedback controllers, thereby providing a practical and effective control method for complex dynamical networks. An estimation method of exponential convergence rate is also presented. Finally, the effectiveness of the proposed criteria is verified through numerical simulations.

Generalized Outer Synchronization of Stochastic Neural Networks With Time-Varying Delays

Abstract In this paper, generalized outer synchronization between two different stochastic coupled complex dynamical networks with time-varying delays has been investigated. A novel controller is given and the stochastic invariance principle is applied. A stochastic disturbance which is described in term of a Brownian motion are considered in complex dynamical networks. Moreover, some sufficient conditions are derived to ensure generalized outer synchronization of stochastic neural networks. Surprisingly, it is found that complex networks with different structure can be synchronized.

Global synchronization of nonlinear coupled complex dynamical networks with information exchanges at discrete-time

This paper studies the problem of synchronization for a class of complex networks with discrete-time couplings. The intrinsic local dynamical behaviors of the nodes in the complex networks are varied continuously while the manners of information interaction between every two different nodes are discrete time-varying rather than proceeded continuously, that is, the communications of the nodes only active at some discrete instants. Similar to the sampled data control systems, we convert the discrete time coupling issue into an effective time-varying delayed coupling network. By constructing the Lyapunov function skillfully, sufficient conditions are derived to guarantee the realization of the synchronization pattern for all initial values based on the Lyapunov stability theorem and linear matrix inequalities. What is more, the maximum allowable sampling period for communication is obtained through a optimization problem. Numerical simulations are also exploited to demonstrate the effectiveness and validity of the main result.

Synchronisation of complex dynamical networks with different dynamics of nodes via decentralised dynamical compensation controllers

This paper investigates the synchronisation of nonlinear coupled complex dynamical networks with different nonlinear nodes and different orders by using decentralised dynamical compensation controllers. We propose a dynamical network mathematical model with similar nonlinear nodes, whose dimensions are different. For this kind of network model, the decentralised dynamical compensation controllers are designed for the state synchronisation of the coupled nodes. In addition, the synchronisation manifold is defined as an invariant manifold, which is regarded as the generalised case of dynamical networks with the same nodes’ dynamics. Furthermore, some stability criteria for the synchronisation are derived by means of rigorous theoretical analysis. Finally, numerical examples are presented to verify the effectiveness of the obtained theoretical results.