Uncertain Complex Networks Research Articles

Parameter identification and adaptive–impulsive synchronization of uncertain complex networks with nonidentical topological structures

In this paper, we integrate impulsive control and adaptive control methods, based on the stability theory of impulsive differential equations, synchronization of uncertain complex networks with nonidentical topological structures is investigated. By designing effective adaptive–impulsive controllers, we achieve synchronization criteria of uncertain complex networks with nonidentical topological structures, parameter identification is realized simultaneously as the synchronization occurs. Moreover, the case of identical topological structures is considered. Finally, numerical simulations are given to illustrate the theoretical results.

Exponential Outer Synchronization between Two Uncertain Time-Varying Complex Networks with Nonlinear Coupling

This paper studies the problem of exponential outer synchronization between two uncertain nonlinearly coupled complex networks with time delays. In order to synchronize uncertain complex networks, an adaptive control scheme is designed based on the Lyapunov stability theorem. Simultaneously, the unknown system parameters of uncertain complex networks are identified when exponential outer synchronization occurs. Finally, numerical examples are provided to demonstrate the feasibility and effectiveness of the theoretical results.

Mean square modified function projective synchronization of uncertain complex network with multi-links and stochastic perturbations

In this paper, it is mainly concerned with the issue of mean square modified function projective synchronization of uncertain complex network with multi-links and stochastic perturbations. The uncertain terms are the unknown topological structure which exists inside the complex network and the external noise is imposed to the network. In order to achieve the mean square modified function projective synchronization of complex dynamical network, a strict feedback controller and novel adaptive control laws are designed based on Lyapunov stability theory, inequality techniques, and the properties of the Weiner process to obtain several novel synchronization criterion. Furthermore, the effectiveness of the proposed control scheme is validated by numerical simulations.

Adaptive Control and Synchronization of Uncertain Complex Networks

Recently, synchronization of complex networks has been a focus subject of technology fields. In this paper, we consider the adaptive control and synchronization of uncertain complex networks. By using the adaptive control techniques with the linear feedback updated law and the well-known invariant principle on dynamical system theory, some simple yet generic criteria are derived. Furthermore, the result is applied to typical chaotic cellular neural networks (CNN). Finally, numerical simulations are presented to demonstrate the feasibility and effectiveness of the proposed techniques.

Cluster synchronization of overlapping uncertain complex networks with time-varying impulse disturbances

This paper addresses the scheme of cluster synchronization of overlapping uncertain complex networks with time-varying impulse disturbances. Many existing works on cluster synchronization focus on synchronizing and desynchronizing impulses separately, but the effects of two types of impulses are rarely observed. Here, we present the analysis of the two types (time-varying impulses) in complex networks. Furthermore, by means of stochastic stability theorem, sufficient conditions for guaranteeing the realization of cluster synchronization are derived. The network topology is assumed to be overlapping community, which includes an overlapping sub community with different dynamic behavior due to its identity (community). Finally, numerical examples are exploited to verify the correctness and effectiveness of theoretical results.

Adaptive Synchronization of Fractional Neural Networks with Unknown Parameters and Time Delays

In this paper, the parameters identification and synchronization problem of fractional-order neural networks with time delays are investigated. Based on some analytical techniques and an adaptive control method, a simple adaptive synchronization controller and parameter update laws are designed to synchronize two uncertain complex networks with time delays. Besides, the system parameters in the uncertain network can be identified in the process of synchronization. To demonstrate the validity of the proposed method, several illustrative examples are presented.

Cluster synchronization of uncertain complex networks with desynchronizing impulse

Cluster synchronization of nonlinear uncertain complex networks with desynchronizing impulse is explored. First of all, a feedback controller is employed, based on the Lyapunov stability theorem and Lipschitz condition, to guarantee that the uncertain complex networks with desynchronizing impulse synchronize with an object trajectory. Furthermore, a synchronizing impulse controller is presented, which is more efficiently and directly used to achieve the cluster synchronization. Finally, numerical examples are examined to show the effectiveness of the proposed methods.

Applied-Information Technology in Robust Synchronization of Uncertain Fractional-Order Complex Networks

This paper deals with robust synchronization of a class of uncertain fractional-order complex networks. Robust stability criteria of uncertain fractional-order system with is investigated based on LMI technique. Furthermore, robust synchronization of uncertain fractional-order complex networks is discussed based on the LMI technique. Finally, numerical example is given to illustrate the effectiveness of the proposed methods.

Spatiotemporal chaos synchronization between uncertain complex networks with diverse structures

Spatiotemporal chaos synchronization between uncertain complex networks with diverse structures is investigated. The identification law of unknown parameters and the adaptive law of the configuration matrix element in state equations of network nodes are determined based on stability theory, and the conditions of realizing spatiotemporal chaos synchronization between uncertain complex networks with different structures are discussed and obtained. Further, the Fisher–Kolmogorov system with spatiotemporal chaotic behavior is taken as the nodes of drive and response networks to imitate the experiment. It is found that the synchronization performance between two networks is very stable.

Robust adaptive synchronization of uncertain complex networks with multiple time‐varying coupled delays

In this article, the synchronization problem of uncertain complex networks with multiple coupled time‐varying delays is studied. The synchronization criterion is deduced for complex dynamical networks with multiple different time‐varying coupling delays and uncertainties, based on Lyapunov stability theory and robust adaptive principle. By designing suitable robust adaptive synchronization controllers that have strong robustness against the uncertainties in coupling matrices, the all nodes states of complex networks globally asymptotically synchronize to a desired synchronization state. The numerical simulations are given to show the feasibility and effectiveness of theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 20: 62–73, 2015

Hybrid adaptive and impulsive synchronization of uncertain complex networks with delays and general uncertain perturbations

This paper is concerned with the problem of asymptotic synchronization for a class of uncertain complex networks with delays and general uncertain perturbations. In order to cope with the bad effects generated by the uncertain perturbations, a novel hybrid adaptive and impulsive controller is designed such that the complex network can be asymptotically synchronized onto an isolate chaotic system with uncertain perturbations. All the perturbations can be different from each other. On the basis of a new lemma, squeezing rule, and Lyapunov–Krasovskii functionals, several sufficient conditions guaranteeing the realization of the synchronization goal are derived. It is shown that the designed hybrid controllers exhibit powerful robustness. Some existing results are improved and extended. Numerical simulations verify the effectiveness of the theoretical results and the robustness of the new controller.

Topology Identification and Adaptive Synchronization of Fractional-Order Complex Networks

This paper investigates topology identification and adaptive synchronization of uncertain complex networks with fractional-order systems nodes. In comparison with those of the integerorder chaotic system nodes, this method is more efficiently which can enlarge the key space. Moreover, the uncertain network topological structure is identified simultaneously in the process of synchronization. Illustrative examples are presented to demonstrate the application of the theoretical results.

Erratum to: Parameter identification and synchronization of uncertain general complex networks via adaptive-impulsive control

Complex networks have been judiciously developed during the last decades. Much attention has been given to investigate the synchronization of complex networks in recent years. In this paper, by constructing a drive network and a suitable impulsively controlled slave network, several synchronization criteria for the uncertain complex networks have been obtained based on the adaptive-impulsive method. The tracking parameters are realized simultaneously as the synchronization occurs. Particularly, our hypotheses and the proposed adaptive-impulsive control laws for network synchronization are simple and can be readily applied in practical applications. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed synchronization criteria.

Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties

The problem of robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties is investigated in this article. It is only assumed that the upper normal bound of uncertain inner and outer coupling matrices is positive but its concrete structure is not also required to be known. The time‐varying coupling delay is a any nonnegative continuous and bounded function and not require its derivative to be less than one, that is, general time‐varying coupling delays and uncertainties. For such a class of uncertain complex networks, a new synchronization scheme is presented by a class of continuous memoryless robust decentralized adaptive synchronization controllers. It is also shown that the synchronization error dynamics of uncertain complex networks can be guaranteed as uniformly exponentially convergent toward a ball that can be as small as desired. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of proposed complex networks synchronization schemes. © 2013 Wiley Periodicals, Inc. Complexity 19: 10–26, 2014

Synchronization-based topology identification of uncertain stochastic delay complex networks

In this paper, topology identification of general weighted complex network with time-varying delay and stochastic perturbation, which is a zero-mean real scalar Wiener process, is investigated. Based on the adaptive-feedback control method, the stochastic Lyapunov stability theory and the ito formula, some synchronous criteria are established, which guarantee the asymptotical mean square synchronization of the drive network and the response network with stochastic disturbances, as well as identify the topological structure of the uncertain general drive complex network. Finally, numerical simulations are presented to verify the correctness and effectiveness of the proposed scheme.

Outer synchronization between uncertain complex networks based on backstepping design

In this paper, the outer synchronization between uncertain networks is investigated using the backstepping design. The adaptive laws of uncertain parameters and the structure of control input in the node of response network are determined based on the stability theory. The outer synchronization between networks can be realized only by putting a control input on one node of response network. Further, the effect of the synchronization principle is verified through a simulation experiment.

Robust projective outer synchronization of coupled uncertain fractional-order complex networks

AbstractIn this work, we propose a novel projective outer synchronization (POS) between unidirectionally coupled uncertain fractional-order complex networks through scalar transmitted signals. Based on the state observer theory, a control law is designed and some criteria are given in terms of linear matrix inequalities which guarantee global robust POS between such networks. Interestingly, in the POS regime, we show that different choices of scaling factor give rise to different outer synchrony, with various special cases including complete outer synchrony, anti-outer synchrony and even a state of amplitude death. Furthermore, it is demonstrated that although stability of POS is irrelevant to the inner-coupling strength, it will affect the convergence speed of POS. In particular, stronger inner synchronization can induce faster POS. The effectiveness of our method is revealed by numerical simulations on fractional-order complex networks with small-world communication topology.

Robust synchronization for stochastic delayed complex networks with switching topology and unmodeled dynamics via adaptive control approach

In this paper, the robust synchronization problem for a class of stochastic delayed complex networks with switching topology and unmodeled dynamics is investigated by using the adaptive control scheme. Different from some existing uncertain complex network models, the uncertain terms in the complex networks are only needed to be bounded. Based on the stability theory of stochastic delayed differential equation, a novel adaptive controller which ensures that all the nodes in the complex networks robustly synchronize with the target node is derived. Finally, a numerical example is provided to show the effectiveness of the proposed method.

Parameter estimation and topology identification of uncertain fractional order complex networks

This paper focuses on a significant issue in the research of fractional order complex network, i.e., the identification problem of unknown system parameters and network topologies in uncertain complex networks with fractional-order node dynamics. Based on the stability analysis of fractional order systems and the adaptive control method, we propose a novel and general approach to address this challenge. The theoretical results in this paper have generalized the synchronization-based identification method that has been reported in several literatures on identifying integer order complex networks. We further derive the sufficient condition that ensures successful network identification. An uncertain complex network with four fractional-order Lorenz systems is employed to verify the effectiveness of the proposed approach. The numerical results show that this approach is applicable for online monitoring of the static or changing network topology. In addition, we present a discussion to explore which factor would influence the identification process. Certain interesting conclusions from the discussion are obtained, which reveal that large coupling strengths and small fractional orders are both harmful for a successful identification.

Robust synchronization of a class of uncertain complex networks via discontinuous control

We propose robust controller designs to synchronize networks with uncertainties in their node dynamics and their connections. We consider two situations: in the first, we assume that the effect of uncertainties vanishes as synchronization is achieved. In the second, disturbances are assume nonvanishing but bounded. To achieve robust synchronization on these situations, we design local feedback controllers, which are smooth in the first case, and discontinuous in the latter. These designs allow us to establish synchronization criteria for this class of uncertain dynamical networks. We use numerical experiments to illustrate our results.