LMI Based Guaranteed Cost Synchronization for Nonlinear Complex Dynamical Networks with Similar Nodes and Coupling Time-varying Delay

In this paper, mixed outer synchronization between two different complex dynamical networks without and with time-varying delayed couplings is investigated. By pinning only a fraction of the nodes in the response network, some effective mixed outer synchronization criteria are obtained based on the Lyapunov stability theory. As a result, the mixed outer synchronization between two complex networks is achieved. Then, in the view of the generalized time-varying delayed different inequalities, some sufficient conditions for mixed outer exponential synchronization are derived by imposing the impulsive controllers to the nodes of the corresponding response network. Finally, some numerical simulations are presented to demonstrate the effectiveness and feasibility of the results we obtained in this paper.

SummaryDetermining the centrality of nodes in complex networks provides practical benefits in many areas such as detecting influencer nodes, viral marketing, and preventing the spread of rumors. On the other hand, there is no consensus for the definition of centrality. Therefore, different centrality measures such as degree, closeness, and betweenness have been developed to measure the centrality of a node. However, each centrality measure highlights the various characteristics of the nodes in the network from its own point of view. This causes each centrality measure to rank the nodes in a different order. In recent years, researchers have focused on approaches that combine multiple centrality measures. Thus, the perspectives of different centrality measures can be considered simultaneously. In this study, we have proposed a fast and efficient method using the analytic hierarchy process and entropy weighting to combine multiple centrality measures. We tested the proposed method with synthetic and real datasets and compared the results with those of state‐of‐the‐art methods. The experimental results showed the proposed method to be competitive with these advanced methods, whereas it performed much better than the other methods in terms of computational speed. This indicated that our proposed method could be applied to large and dynamic complex networks.

SummaryThe issues of cluster synchronization and state estimation for a class of nonlinear complex dynamical networks are concurrently focused in this study. In precise, led by the design of complex dynamical networks, a proportional integral‐based observer is implemented for achieving robustness, by the virtue of which the states of examined networks are estimated. Thereupon, a proportional integral observer‐based hybrid triggered control scheme is proposed, wherein, the switch‐over between time‐ and event‐ triggered scheme is governed through a Bernoulli distributed random variable. Further, with the application of mixed and passivity performance technique, the external disturbances for the addressed complex dynamical networks are reduced. Based on the Lyapunov stability theory, the requisite sufficient conditions in respect of linear matrix inequalities are provided which ensures the discussed complex dynamical network's synchronization phenomenon. In a further, the presented criteria are exploited for the attainment of required controller, proportional and integral gain matrices. In conclusion, the applicability of proposed results and efficacy of the undertaken strategy are evidently proven with the illustration of two numerical examples with Chua's circuit and Goodwin oscillator model.

This paper focuses on the problem of exponential synchronization of complex dynamical networks (CDNs) with time-varying coupling delay and sampled-data. An improved synchronization criterion is derived for the considered CDNs in terms of the free-weighting matrix method and input delay approach. The design method of the desired sampled-data controller is proposed. The derived result is numerically shown to be less conservative than existing one.

Influential nodes refer to the ability of a node to spread information in complex networks. Identifying influential nodes is an important problem in complex networks which plays a key role in many applications such as rumor controlling, virus spreading, viral market advertising, research paper views, and citations. Basic measures like degree centrality, betweenness centrality, closeness centrality are identifying influential nodes but they are incapable of largescale networks due to time complexity issues. Chen et al. [1] proposed semi-local centrality, which is reducing computation complexity and finding influential nodes in the network. Recently Yang et al. 2020 [2] proposed a novel centrality measure based on degree and clustering coefficient for identifying the influential nodes. Sanjay et al. 2020 [3] gave voterank and neighborhood coreness-based algorithms for finding the influenced nodes in the network. Zhiwei et al. 2019 [4] considered the average shortest path to discover the influenced node in the network. These are the few recent local,global and mixed centralities. In this paper, we show a broad view of recent methods for finding influential nodes in complex networks. It also analyzes the new challenges and limitations for a better understanding of each method in detail. The experimental results based on these methods show better performance compared with existing basic centrality measures.

Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control

Evaluating the importance of nodes in complex networks is an important topic in the research of network characteristics. Its relevant research has a wide range of applications, such as network supervision and rumor control. At present, many methods have been proposed to evaluate the importance of nodes in complex networks, but most of them have the deficiency of one-sided evaluation or too high time complexity. In order to break through the limitations of existing methods, in this paper a novel method of evaluating the importance of complex network nodes is proposed based on Tsallis entropy. This method takes into account both the local and global topological information of the node. It considers the structural hole characteristics and K-shell centrality of the node and fully takes into account the influence of the node itself and its neighboring nodes. To illustrate the effectiveness and applicability of this method, eight real networks are selected from different fields and five existing methods of evaluating node importance are used as comparison methods. On this basis, the monotonicity index, SIR (susceptible-infectious-recovered) model, and Kendall correlation coefficient are used to illustrate the superiority of this method and the relationship among different methods. Experimental results show that this method can effectively and accurately evaluate the importance of nodes in complex networks, distinguish the importance of different nodes significantly, and can show good accuracy of evaluating the node importance under different proportions of nodes. In addition, the time complexity of this method is <inline-formula><tex-math id="M2">\begin{document}$ O({n^2}) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20210979_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20210979_M2.png"/></alternatives></inline-formula>, which is suitable for large-scale complex networks.

Online environments have evolved from the early-stage technical systems to social platforms with social communication mechanisms resembling the interactions which can be found in the real world. Online marketers are using the close relations between the users of social networks to more easily propagate the marketing contents in their advertising campaigns. Such viral marketing campaigns have proven to provide better results than traditional online marketing, hence the increasing research interest in the topic. While the majority of the up-to-date research focuses on maximizing the global coverage and influence in the complete network, some studies have been conducted in the area of budget-constrained conditions as well as in the area of targeting particular groups of nodes. In this paper, a novel approach to targeting multi-attribute nodes in complex networks is presented, in which an MCDA method with various preference weights for all criteria is used to select the initial seeds to best reach the targeted nodes in the network. The proposed approach shows some symmetric characteristics—while the global coverage in the network is decreased, the coverage amongst the targeted nodes grows.

A novel method of evaluating key nodes in complex networks

This paper is concerned with two-layer complex networks with unidirectional interlayer couplings, where the drive and response layer have time-varying coupling delay and different topological structures. An adaptive control scheme is proposed to investigate finite-time mixed interlayer synchronization (FMIS) of two-layer networks. Based on the Lyapunov stability theory, a criterion for realizing FMIS is derived. In addition, several sufficient conditions for realizing mixed interlayer synchronization are given. Finally, some numerical simulations are presented to verify the correctness and effectiveness of theoretical results. Meanwhile, the proposed adaptive control strategy is demonstrated to be nonfragile with the noise perturbation.

The identification of critical nodes in the network is of great significance for the research of the invulnerability and structural stability of complex networks. Most of the existing studies evaluate the importance of nodes in networks from a single structural perspective. Considering the local and global characteristics of the network, an identification algorithm of critical nodes in complex networks based on comprehensive topological importance (CTI) is proposed. The algorithm uses the theory of multiple attribute decision making (MADM) to quantitatively analyze the influence of different attributes on nodes and determine the comprehensive topology importance of nodes, which represents their structural importance in complex networks. Based on two simulation networks and five classical real networks, the proposed algorithm is proved to be superior to DC, LLS, P and WL indexes based on local information and BC indexes based on global information through the change of network efficiency under critical nodes attacking.

This paper deals with the function projective synchronization of two complex dynamic networks with unknown sector nonlinear input, multiple time-varying delay couplings, model uncertainty, and external interferences. Based on Lyapunov stability theory and inequality transformation method, the robust adaptive synchronization controller is designed, by which the drive and response systems can achieve synchronization according to the function scaling factor. Different from some existing studies on nonlinear system with sector nonlinear input, this paper studies the synchronization of two complex dynamic networks when the boundary of sector nonlinear input is unknown. The controller does not include the boundary value of the sector nonlinear input and the time delay term, so it is more practical and relatively easy to implement. The corresponding simulation examples demonstrate the effectiveness of the proposed scheme.

Adaptive projective lag synchronization of uncertain complex dynamical networks with disturbance

This paper studies the problem of sampled-data exponential synchronization of complex dynamical networks (CDNs) with time-varying coupling delay and uncertain sampling. By combining the time-dependent Lyapunov functional approach and convex combination technique, a criterion is derived to ensure the exponential stability of the error dynamics, which fully utilizes the available information about the actual sampling pattern. Based on the derived condition, the design method of the desired sampled-data controllers is proposed to make the CDNs exponentially synchronized and obtain a lower-bound estimation of the largest sampling interval. Simulation examples demonstrate that the presented method can significantly reduce the conservatism of the existing results, and lead to wider applications.

Generalized walks-based centrality measures for complex biological networks