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Complex systems provide an opportunity to analyze the essence of phenomena by studying their intricate connections. The networks formed by these connections, known as complex networks, embody the underlying principles governing the system’s behavior. While complex networks have been previously applied in the field of evolutionary computation, prior studies have been limited in their ability to reach conclusive conclusions. Based on our investigations, we are against the notion that there is a direct link between the complex network structure of an algorithm and its performance, and we demonstrate this experimentally. In this paper, we address these limitations by analyzing the dynamic complex network structures of five algorithms across three different problems. By incorporating mathematical distributions utilized in prior research, we not only generate novel insights but also refine and challenge previous conclusions. Specifically, we introduce the biased Poisson distribution to describe the algorithm’s exploration capability and the biased power-law distribution to represent its exploitation potential during the convergence process. Our aim is to redirect research on the interplay between complex networks and evolutionary computation towards dynamic network structures, elucidating the essence of exploitation and exploration in the black-box optimization process of evolutionary algorithms via dynamic complex networks.

This paper investigates the drive-response synchronization problem of Takagi–Sugeno fuzzy hidden Markov jump complex dynamical networks. More precisely, a novel asynchronous synchronization control strategy is developed for coping with mismatched hidden jumping modes. Furthermore, the neural network is adopted with online learning laws for unknown function approximation. By taking advantage of Lyapunov method, sufficient conditions are established to ensure mean-square synchronization performance with disturbances. Based on the synchronization criterion, asynchronous controller gains are designed in terms of linear matrix inequalities. An illustrative example is finally given to validate the effectiveness of the proposed synchronization techniques.

In this paper, we mainly propose a chaotic secure communication scheme which is based on the synchronization of double-layered and multiple complex dynamical networks. Compared with the previous chaotic secure communication schemes, in which only two chaotic systems or just a single-layer network composed of multiple chaotic systems is used, the introduction of a double-layered and multiple complex networks model composed of many encryption/encryption units can not only reflect the complex characteristics of different nodes, but also can improve the complexity and security of information encryption. By using a clustering method, nodes with the same characteristics belong to the same subnet, while the nodes with different characteristics belong to different ones. The subnets in the transmitter and receiver are one-to-one correspondence and form a pair of matching subnets, but the node size of each subnet can be inconsistent. Each subnet is only responsible for encrypting a certain part of information, and thus, the synchronization between each pair of matching subnets plays a crucial role on the correct recovery of information. Multiple encryption/decryption units operating in parallel way can speed up the encryption of information, and the key space can grow with the number of nodes in the transmitter. The proposed scheme utilizes the chaotic signals generated by many chaotic systems as the key sequences and adopts the one-time-one-cipher encryption method. Moreover, this scheme is not subject to the constraint that the amplitude of the encrypted signal should be much smaller than that of the chaotic signal, and it is particularly suitable for the big data encryption. Both theoretical analysis and numerical simulation demonstrate the feasibility and effectiveness of the proposed scheme.

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.

The mean square synchronization problem of the complex dynamical network (CDN) with the stochastic link dynamics is investigated. In contrast to previous literature, the CDN considered in this paper can be viewed as consisting of two subsystems coupled to each other. One subsystem consists of all nodes, referred to as the nodes subsystem, and the other consists of all links, referred to as the network topology subsystem, where the weighted values can quantitatively reflect changes in the network’s topology. Based on the above understanding of CDN, two vector stochastic differential equations with Brownian motion are used to model the dynamic behaviors of nodes and links, respectively. The control strategy incorporates not only the controller in the nodes but also the coupling term in the links, through which the CDN is synchronized in the mean-square sense. Meanwhile, the dynamic stochastic signal is proposed in this paper, which is regarded as the auxiliary reference tracking target of links, such that the links can track the reference target asymptotically when synchronization occurs in nodes. This implies that the eventual topological structure of CDN is stochastic. Finally, a comparison simulation example confirms the superiority of the control strategy in this paper.

This paper focuses on the finite-time synchronization problem for a kind of general complex networks with intrinsic time-varying delays and hybrid couplings (i.e., containing current-state couplings and time-varying delay couplings). By designing a simple discontinuous state feedback controller and using strict analytical techniques, several synchronization criteria are proposed to guarantee that the complex dynamical networks can be synchronized onto an isolated chaotic system in finite time. Besides, the upper bound of the synchronization time could be estimated, which is dependent on the initial values of the system as well as the delays. Then, some finite-time synchronization criteria about special cases of the complex networks are also obtained. Here, the coupling configuration matrices are not required to be symmetric or irreducible in all cases. Finally, numerical examples are provided to demonstrate the correctness of our theoretical results.

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.

This paper examines the synchronization problem of fractional-order complex dynamical networks (FCDNs) against input saturation and time-varying coupling by using a fault-tolerant control scheme. Precisely, the occurrence of coupling delay assumed is considered to be random, which is characterized by stochastic variables that obeys the Bernoulli distribution properties, and the actuator fault values are represented by a normally distributed stochastic random variable. The main aim of this paper is to propose the fault-tolerant fractional-order controller such that for given any initial condition, the state trajectories of considered FCDN are forced to synchronize asymptotically to the reference node. Based on the linear matrix inequality technique and Lyapunov stability theorem, a new set of sufficient conditions is established to not only guarantee mean-square asymptotic synchronization of the resulting closed-loop system but also cover the issues of actuator saturation and actuator faults. Moreover, the obtained sufficient conditions can help to enlarge the estimation about the domain of attraction for the closed-loop system. Finally, to show the advantages and effectiveness of the developed control design, numerical simulations are carried out on both Lorenz and Chen type FCDNs.

This paper is concerned with the global synchronization in fixed time for semi-Markovian switching complex dynamical networks with hybrid couplings and time-varying delays in the presence of disturbances. Firstly, the property with respect to the global stability in fixed time is developed for semi-Markovian switching nonlinear systems. Subsequently, a novel sliding manifold with double integration is presented based on the proposed principle of convergence in fixed time. Under the designed sliding mode controller, the state trajectory of synchronization error system is driven to the prescribed sliding manifold in fixed time. In addition, the global stability in fixed time of sliding mode dynamics is proved analytically. By means of the stochastic Lyapunov–Krasovskii functional approach, the synchronization condition is established in terms of linear matrix inequalities; moreover, the stochastic fixed settling-time can be determined to any desired values in advance, via the configuration of parameters in the proposed controller. Finally, two numerical examples are provided to demonstrate the validity of the theoretical results and the feasibility of the proposed approach.

Secure synchronization control is critical for information interaction in complex dynamical networks suffering from malicious attacks. This paper addresses the observer-based secure synchronization control of directed complex-valued dynamical networks (DCDNs) with or without parameter perturbations under link attacks. To overcome the unavailablity of node-states in some circumstances, observer is designed to estimate the true node-states. Differing from previously observer-based synchronization control problems for DCDNs, link attacks disrupt communication channels and lead to disconnected topologies of the communication networks. Moreover, regardless of whether the impacts of link attacks on the control and measurement channels are identical or nonidentical, by applying the Lyapunov method and inequality techniques in the complex field, several sufficient criteria are derived for ensuring the secure synchronization of DCDNs in the presence of link attacks. Eventually, illustrative examples are presented to substantiate the effectiveness of the proposed theoretical strategies.