Fixed-Time Synchronization Control of Delayed Dynamical Complex Networks

Fixed-time synchronization problem for delayed dynamical complex networks is explored in this paper. Compared with some correspondingly existed results, a few new results are obtained to guarantee fixed-time synchronization of delayed dynamical networks model. Moreover, by designing adaptive controller and discontinuous feedback controller, fixed-time synchronization can be realized through regulating the main control parameter. Additionally, a new theorem for fixed-time synchronization is used to reduce the conservatism of the existing work in terms of conditions and the estimate of synchronization time. In particular, we obtain some fixed-time synchronization criteria for a type of coupled delayed neural networks. Finally, the analysis and comparison of the proposed controllers are given to demonstrate the validness of the derived results from one numerical example.

Fixed-Time Synchronization for Dynamical Complex Networks with Nonidentical Discontinuous Nodes

This article investigates the fixed-time synchronization issue for linearly coupled complex networks with discontinuous nonidentical nodes by employing state-feedback discontinuous controllers. Based on the fixed-time stability theorem and linear matrix inequality techniques, novel conditions are proposed for concerned complex networks, under which the fixed-time synchronization can be realized onto any target node by using a set of newly designed state-feedback discontinuous controllers. To some extent, this article extends and improves some existing results on the synchronization of complex networks. In the final numerical example section, the Chua circuit network is introduced to indicate the effectiveness of our method by showing its fixed-timely synchronization results with the proposed control scheme.

Community Detection of Dynamic Complex Networks in Stock Markets Using Hybrid Methods (RMT‐CN‐LPAm+ and RMT‐BDM‐SA)

A stock market represents a large number of interacting elements, leading to complex hidden interactions. It is very challenging to find a useful method to detect the detailed dynamical complex networks involved in the interactions. For this reason, we propose two hybrid methods called RMT-CN-LPAm+ and RMT-BDM-SA (RMT, random matrix theory; CN, complex network; LPAm+, advanced label propagation algorithm; BDM, block diagonal matrix; SA, simulated annealing). In this study, we investigated group mapping in the S&P 500 stock market using these two hybrid methods. Our results showed the good performance of the proposed methods, with both the methods demonstrating their own benefits and strong points. For example, RMT-CN-LPAm+ successfully identified six groups comprising 485 involved nodes and 17 isolated nodes, with a maximum modularity of 0.62 (identified more groups and displayed more maximum modularity). Meanwhile, RMT-BDM-SA provided useful detailed information through the decomposition of matrix C into Cm (market-wide), Cg (group), and Cr (noise). Both hybrid methods successfully performed very detailed community detection of dynamic complex networks in the stock market.

Synchronization in Time-Varying and Evolving Complex Networks

In this contribution, we present the synchronization in dynamical complex networks with varying couplings. We identify two kinds of variations—(i) Non autonomous (Time-varying) couplings: where the coupling strength depends exclusively on time, (ii) Autonomous or Varying couplings (evolution) where the coupling strength depends on the behavior of the interconnected systems. The coupling strength in (i) is exogenous whereas in (ii) the coupling strength is endogenous and is defined by the states of the systems in the nodes. The exponential stability of the synchronization is ensured for the non autonomous couplings, due to the imposition of the coupling strength. Whereas, in the case of evolutionary couplings the exponential stability of the synchronization is not guaranteed for all time, due to the couplings are not controlled or imposed. We present an overview of these features in complex networks and illustrated by means of numerical examples.