Synchronization Of Complex Dynamical Networks Research Articles

Fixed-time sliding mode controller design for synchronization of complex dynamical networks

This paper investigates the fixed-time synchronization of complex dynamical networks with nonidentical nodes in the presence of bounded uncertainties and disturbances using sliding mode control technique. Firstly, a novel sliding surface is introduced and fixed-time stability of the sliding mode dynamics is proven by benefiting from Gudermannian function. Then, a novel sliding mode controller is proposed whereby fixed-time stability of the reaching mode is guaranteed. The outstanding feature of the proposed controller is that fixed convergence times of reaching and sliding modes are independent design parameters explicitly existing in the control law. This allows us not only to set the reaching time of reaching mode and settling time of sliding mode at any desired values in advance but also to adjust them independent of each other and in the most straightforward possible way. Finally, simulation results are reported in order to show the effectiveness of the proposed controller.

Improved algorithm of spectral coarse graining method of complex network

Complex network as a key approach to understanding many complex systems, such as biological, chemical, physical, technological and social systems, is ubiquitous in nature and society. Synchronization of large-scale complex networks is one of the most important issues in network science. In the last two decades, much attention has been paid to the synchronization of complex dynamic networks, especially the meso-scale networks. However, many real networks consist of even hundreds of millions of nodes. Analyzing the synchronization of such large-scale coupled complex dynamic networks often generate a large number of coupled differential equations, which may make many synchronization algorithms inapplicable for meso-scale networks due to the complexities of simulation experiments. Coarse graining method can map the large-scale networks into meso-scale networks while preserving some of topological properties or dynamic charac-teristics of the original network. Especially, the spectral coarse-graining scheme, as a typical coarse graining method, is proposed to reduce the network size while preserving the synchronization capacity of the initial network. Nevertheless, plenty of studies demonstrate that the components of eigenvectors for the eigenvalue of the coupling matrix, which can depict the ability to synchronizing networks, distribute unevenly. Most of the components distribute concentrically and the intervals are small, while some other components distribute dispersedly and the intervals are large, which renders the applications of original spectral coarse graining method unsatisfactory. Inspired by the adaptive clustering, we propose an improved spectral coarse graining algorithm, which clusters the same or the similar nodes in the network according to the distance between the components of eigenvectors for the eigenvalue of network coupling matrices, so that the nodes with the same or the similar dynamic properties can be effectively clustered together. Compared with the original spectral coarse graining algorithm, this method can improve the accuracy of the result of clustering. Meanwhile, our method can greatly reduce algorithm complexity, and obtain better spectral coarse graining result. Finally, numerical simulation experiments are implemented in four typical complex networks: NW network, ER network, BA scale-free network and clustering network. The comparison of results demonstrate that our method outperforms the original spectral coarse graining approach under various criteria, and improves the effect of coarse graining and the ability to synchronize networks.

Finite-Time Synchronization of Complex Dynamical Networks with Time-Varying Delays and Nonidentical Nodes

In this paper, we investigated the finite-time synchronization (FTS) problem for a class of time-delayed complex networks with nonidentical nodes onto any uniformly smooth state. By employing the finite-time stability theorem and designing two types of novel controllers, we obtained some simple sufficient conditions for the FTS of addressed complex networks. Furthermore, we also analyzed the effects of control variables on synchronization performance. Finally, we showed the effectiveness and feasibility of our methods by giving two numerical examples.

Passivity and Output Synchronization of Complex Dynamical Networks With Fixed and Adaptive Coupling Strength.

This paper considers a complex dynamical network model, in which the input and output vectors have different dimensions. We, respectively, investigate the passivity and the relationship between output strict passivity and output synchronization of the complex dynamical network with fixed and adaptive coupling strength. First, two new passivity definitions are proposed, which generalize some existing concepts of passivity. By constructing appropriate Lyapunov functional, some sufficient conditions ensuring the passivity, input strict passivity and output strict passivity are derived for the complex dynamical network with fixed coupling strength. In addition, we also reveal the relationship between output strict passivity and output synchronization of the complex dynamical network with fixed coupling strength. By employing the relationship between output strict passivity and output synchronization, a sufficient condition for output synchronization of the complex dynamical network with fixed coupling strength is established. Then, we extend these results to the case when the coupling strength is adaptively adjusted. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of the proposed criteria.

Adaptive synchronization of complex dynamical networks with bounded delay feedback controller

This paper is concerned with adaptive synchronization of the general complex dynamical network with bounded delay feedback controller in finite-time. Different from the existing related results, the design of feedback controller is always bounded. First, an effective criterion is derived to realize synchronization of complex dynamical networks with general bounded delay controller in finite-time, since it is difficult to implement in practical applications, adaptive delay bounded feedback controller is proposed to compensate this defect, and adaptive time-varying delay bounded feedback controller is also be discussed. Finally, a numerical example is provided to verify the theoretical results established in this paper.

Nonfragile Exponential Synchronization of Delayed Complex Dynamical Networks With Memory Sampled-Data Control

This paper considers nonfragile exponential synchronization for complex dynamical networks (CDNs) with time-varying coupling delay. The sampled-data feedback control, which is assumed to allow norm-bounded uncertainty and involves a constant signal transmission delay, is constructed for the first time in this paper. By constructing a suitable augmented Lyapunov function, and with the help of introduced integral inequalities and employing the convex combination technique, a sufficient condition is developed, such that the nonfragile exponential stability of the error system is guaranteed. As a result, for the case of sampled-data control free of norm-bound uncertainties, some sufficient conditions of sampled-data synchronization criteria for the CDNs with time-varying coupling delay are presented. As the formulations are in the framework of linear matrix inequality, these conditions can be easily solved and implemented. Two illustrative examples are presented to demonstrate the effectiveness and merits of the proposed feedback control.

Synchronization for complex dynamical networks with mixed mode-dependent time delays

In this paper, the problem of synchronization control is investigated for complex dynamical networks with discrete intervals and distributed time-varying delays. The main thing is to design a properly pinning controller, for which the error system of complex dynamical networks is asymptotically stable. Based on the theory of Lyapunov stability and linear matrix inequality, the suitable Lyapunov-Krasovskii functional is constructed in terms of the Kronecker product, and then we obtain a novel synchronization criterion. Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.

Finite-time H∞ synchronization for complex dynamical networks with mixed mode-dependent time delays

This paper investigated the finite-time H∞ synchronization control for complex dynamical networks with mixed mode-dependent time delays. The complex dynamical networks system contains the general coupling term and the time-delay coupling term. The state feedback control is designed to ensure that the complex dynamical networks system is finite time H∞ synchronized. The sufficient conditions are established in the form of linear matrix inequalities by constructing a suitable Lyapunov–Krasovskii functional with triple integral terms and using Kronecker product. In the last, a numerical example is given to demonstrate the effectiveness of proposed approach.

Synchronization of complex dynamical networks on time scales via Wirtinger-based inequality

A new Wirtinger-based inequality on time scales which can unify the continuous and discrete ones is studied in this paper. By using the new inequality, a new approach to synchronization of complex dynamical networks with discrete time delays on time scales is given. To illustrate the effectiveness of our results, an example is given.

Synchronization of complex dynamical networks with hybrid coupling delays on time scales by handling multitude Kronecker product terms

The problem of synchronization is studied for complex dynamical networks with hybrid coupling delays on time scales. The hybrid coupling delays consist of both discrete and distributed coupling delays. Some novel and useful synchronization criteria of complex dynamical networks are derived based on stability theory of error dynamical system. By employing the standard Lyapunov–Krasovskii functional, matrix expansion method to handle multitude Kronecker product terms and the modified Jensen’s inequalities on time scale, new sufficient conditions guaranteeing the global exponential stability of the origin of complex dynamical networks are established interms of linear matrix inequality (LMI). Numerical examples are included to demonstrate the effectiveness of the proposed method.

Synchronization Criteria for Complex Dynamical Networks with State and Coupling Time‐Delays

AbstractThis paper is concerned with the problem of synchronization of complex dynamical networks with state and coupling time‐delays. Therefore, larger class and more complicated complex dynamical networks could be considered for the synchronization problem. Based on the Lyapunov‐Krasovskii functional, some delay‐independent and delay‐dependent criteria are obtained and formulated in the form of linear matrix inequalities (LMIs) to ascertain the synchronization between each node of the complex dynamical network. The effectiveness of the proposed method is illustrated using some numerical simulations.

Lag synchronization of complex dynamical networks with hybrid coupling via adaptive pinning control

Lag synchronization of complex dynamical networks with hybrid coupling via adaptive pinning control

Synchronization of complex dynamical networks via pinning scheme design under hybrid topologies

In this paper, the synchronization problem of complex networks is investigated by pinning control method. A kind of novel hybrid topologies is presented, which includes directed network and undirected network. Under the hybrid topologies, the pinning controllers on the chosen nodes of undirected network are designed to reach synchronization behavior with convex combination of the nodes in direct network. The synchronization criterion is established for reaching pinning control on networks. The results can also extend to networks of networks. The pinning scheme is designed by Cholesky Decomposition and triangularization, which shows that the nodes with low degrees and high degrees should be controlled.

Fast synchronization of complex dynamical networks with time-varying delay via periodically intermittent control

The fast synchronization problem for a class of complex dynamical networks with time varying delay by means of periodically intermittent control is studied. Based on the finite-time stability theory and periodically intermittent control technique, some sufficient synchronization criteria are obtained to guarantee the fast synchronization. Furthermore, the essential condition for guaranteeing periodically intermittent control realized in finite time is given in this paper. Finally, two examples are illustrated to verify the proposed theoretical results.

Complete characterization of the stability of cluster synchronization in complex dynamical networks.

Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted to admit global synchronization, a condition called Laplacian coupling. Many networks exhibit incomplete synchronization, where two or more clusters of synchronization persist, and computational group theory has recently proved to be valuable in discovering these cluster states based on the topology of the network. In the important case of Laplacian coupling, additional synchronization patterns can exist that would not be predicted from the group theory analysis alone. Understanding how and when clusters form, merge, and persist is essential for understanding collective dynamics, synchronization, and failure mechanisms of complex networks such as electric power grids, distributed control networks, and autonomous swarming vehicles. We describe a method to find and analyze all of the possible cluster synchronization patterns in a Laplacian-coupled network, by applying methods of computational group theory to dynamically equivalent networks. We present a general technique to evaluate the stability of each of the dynamically valid cluster synchronization patterns. Our results are validated in an optoelectronic experiment on a five-node network that confirms the synchronization patterns predicted by the theory.

Pinning sampled‐data synchronization of complex dynamical networks with Markovian jumping and mixed delays using multiple integral approach

This study deals with the pinning synchronization problem for complex dynamical networks (CDNs) with Markovian jumping parameters and mixed delays under sampled‐data control technique. The mixed delays cover both discrete and distributed delays. The Markovian jumping parameters are modeled as a continuous‐time, finite‐state Markov chain. The sufficient conditions for asymptotic synchronization of considered networks are obtained by utilizing novel Lyapunov‐Krasovskii functional and multiple integral approach. The obtained criteria is formulated in terms of LMIs, which can be checked for feasibility by making use of available softwares. Lastly, numerical simulation results are presented to validate the advantage of the propound theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 622–632, 2016

Hybrid time-varying delay projective synchronization in complex dynamical networks

In this paper, a hybrid time-varying delay projective synchronization method for a complex dynamical network is proposed using a hybrid feedback controller. The existing synchronous errors of the delay projective synchronization are constant. However, the synchronous errors of the time-varying delay projective synchronization show time-varying delay. The time-varying delay projective synchronization improves the delay projective synchronization and the different component variables of the system of the node achieve a different time-varying delay projective synchronization. This paper researches the hybrid time-varying delay projective synchronization of two different types of complex dynamical network. Numerical simulations are given to demonstrate the effectiveness of the proposed synchronization scheme.

Discrete-time systems with random switches: From systems stability to networks synchronization.

In this article, we develop some approaches, which enable us to more accurately and analytically identify the essential patterns that guarantee the almost sure stability of discrete-time systems with random switches. We allow for the case that the elements in the switching connection matrix even obey some unbounded and continuous-valued distributions. In addition to the almost sure stability, we further investigate the almost sure synchronization in complex dynamical networks consisting of randomly connected nodes. Numerical examples illustrate that a chaotic dynamics in the synchronization manifold is preserved when statistical parameters enter some almost sure synchronization region established by the developed approach. Moreover, some delicate configurations are considered on probability space for ensuring synchronization in networks whose nodes are described by nonlinear maps. Both theoretical and numerical results on synchronization are presented by setting only a few random connections in each switch duration. More interestingly, we analytically find it possible to achieve almost sure synchronization in the randomly switching complex networks even with very large population sizes, which cannot be easily realized in non-switching but deterministically connected networks.

Synchronization of complex dynamical networks with time-varying inner coupling

The complex dynamical networks have attracted increasing attention in various fields. The previous models investigated are commonly time invariant; however, the complex networks with time-varying inner coupling are widespread in real world, and their synchronization problems have been rarely studied. We introduce a complex dynamical network model with time-varying inner coupling in this paper. We give the sufficient condition to achieve the exponential synchronization. The numerical simulation results are presented to illustrate the effectiveness of the proposed synchronization criteria.

Stability of fractional nonlinear singular systems and its applications in synchronization of complex dynamical networks

Lyapunov direct method provides a very effective approach to analyze stability of nonlinear systems. However, the well-known Leibniz rule is not suitable for fractional derivatives, which is the main reason that there are few analytical results on stability of fractional systems. This paper deals with stability of fractional nonlinear singular systems and its applications in synchronization of complex dynamical networks. Applying fractional Lyapunov direct method and S-procedure lemma, several sufficient conditions on stability and a simple condition on global synchronization of a class of fractional singular dynamical networks in terms of linear matrix inequalities are derived. Finally, two simple examples are given to show that our proposed methods are simple and convenient in computation.