Synchronization Of Complex Networks Research Articles

Synchronization of complex networks with PID pinning controller

Recently, synchronization of complex networks has been studied deeply; however, most existing works take the standard proportional control strategy approach to pinning controllers, which produces a steady-state error and has a significant time of fluctuation. In order to solve this problem, we propose a new method using the Proportional-Integral-Differential (PID) control to design a pinning control method for synchronization of complex networks. Based on Lyapunov theory, the stability of the network is proved, and sufficient synchronization conditions are obtained. Finally, examples are given to evaluate the effectiveness of the proposed PID pinning method and compare it to the traditional proportional pinning controller and adaptive pinning controller.

Synchronization of stochastic complex networks based on privacy protection

As one of the security issues, privacy protection (PP) has become a research hotspot. The paper studies the synchronization problem of stochastic networks based on PP. First, a synchronization standard for stochastic network with delay is given based on PP. Second, a finite‐time (FnT) synchronization criterion for stochastic network without delay is given based on PP. The PP function of continuous time‐varying function is designed to mask the real state of the controlled complex network before converging to the real value in FnT and infinite time. Finally, the effectiveness of the method discussed in this article was verified through simulation examples.

Global exponential synchronization of complex networks with reaction diffusions and finite distributed delays coupling

This article investigates global exponential synchronization of complex networks with reaction diffusions and finite distributed delays coupling (RDDCCNs). Some restrictions on the coupling configuration matrix and time-varying delays are removed. By constructing comparison functions, utilizing analytic method and inequality techniques, a criterion for exponential synchronization of RDDCCNs is attained under adaptive intermittent control. A corresponding outcome without RDs is also acquired. At last, two simulations are proposed to illustrate validity of the obtained criteria.

Dynamic modulation of external excitation enhance synchronization in complex neuronal network

Understanding and controlling neural network synchronization is crucial for neuroscience in revealing brain functions and addressing neurological disorders. This study explores the innovative use of dynamic learning of synchronization (DLS) technology to enhance synchronization within neuronal networks. Using the Hodgkin-Huxley model across various network topologies, including Erdős-Rényi random graphs, small-world, and scale-free networks, it dynamically adjusts external electrical excitation to study its effects on network synchrony. To further demonstrate the universality of DLS technology, this study also validates the main results using larger-scale networks and the Izhikevich and FitzHugh-Nagumo models. The research quantifies the enhancement of synchrony through DLS, using root-mean-square error (RMSE) and synchronization factors as metrics. Findings show that DLS effectively boosts network synchrony by dynamically adjusting external excitation in response to node differences, significantly in both small-world and scale-free networks, irrespective of synaptic connections. Furthermore, DLS demonstrates potential for targeted synchronization enhancement in specific region of network. This paper highlights DLS technology's effectiveness in modulating external excitation to improve complex neural network synchrony, providing new insights into neural synchronization and information transmission.

Observer-based prescribed-time synchronization and topology identification for complex networks of piecewise-smooth systems with hybrid impulses

Observer-based prescribed-time synchronization and topology identification for complex networks of piecewise-smooth systems with hybrid impulses

Hybrid impulses for almost sure quasi-synchronization of stochastic complex networks: an indefinite Lyapunov function method

. This article studies quasi-synchronization of stochastic complex networks under hybrid impulses. With parameter mismatches, different from the previous quasi-synchronization results in the sense of mean square on stochastic complex networks, almost sure quasi-synchronization is investigated, in which noises have a positive effect on the synchronization. By utilizing the Lyapunov method, stochastic analysis theory, average impulsive interval, and average impulsive gain, we formulate the almost sure quasi-synchronization criteria when the average impulsive interval z 0 satisfies z 0 < + ∞ and z 0 = + ∞ , respectively, where the synchronizing impulses and the desynchronizing impulses are simultaneously considered. It is worth noticing that in our criteria of quasi-synchronization, the mutual restraints among the average impulsive interval, average impulsive gain, and noise intensity are given. Moreover, for the criteria in this article, the piecewise continuous scalar functions cannot only replace the constant coefficient of the upper bound estimation for the diffusion operator of a Lyapunov function in available literature but also even be unbounded, which has wider applications than some existing works. Our corollaries regarding complete synchronization and analyses of the synchronization for stochastic complex networks with aperiodic intermittent noises provide sufficient conditions in closed form. Finally, the theoretical results are applied to a coupled chaotic Lorentz system, and several numerical examples are presented to demonstrate the advantages of the theoretical results.

Clustering Component Synchronization of Nonlinearly Coupled Complex Networks via Pinning Control

In this paper, the problem of clustering component synchronization of nonlinearly coupled complex networks with nonidentical nodes and asymmetric couplings is investigated. A pinning control strategy is designed to achieve the clustering component synchronization with respect to the specified components. Based on matrix analysis and stability theory, clustering component synchronization criteria are established. Two numerical simulations are also provided to show the effectiveness of the theoretical results.

Effects of impulse on prescribed-time synchronization of switching complex networks

The specified convergence time, designated by the user, is highly attractive for many high-demand applications such as industrial robot control, missile guidance, and autonomous vehicles. For the application of neural networks in the field of secure communication and power systems, the importance of prescribed-time synchronization(PTs) and stable performance of the system is more prominent. This paper introduces a prescribed-time controller without the fractional power function and sign function, which can reach synchronization at a prescribed time and greatly reduce the chattering phenomenon of neural networks. Additionally, by constructing synchronizing/desynchronizing impulse sequences, the PTs of switching complex networks(SCN) is achieved with impulse effects, where the time sequences of switching and impulse occurrences in the networks are constrained by the average dwell time. This approach effectively reduces the impact of frequent mode switching on network synchronization, and the synchronization time can be flexibly adjusted within any physically allowable range to accommodate different application requirements. Finally, the effectiveness of the proposed control strategy is demonstrated by two examples.

Novel Controller Design for Finite-Time Synchronization of Fractional-Order Nonidentical Complex Dynamical Networks under Uncertain Parameters

The synchronization of complex networks, as an important and captivating dynamic phenomenon, has been investigated across diverse domains ranging from social activities to ecosystems and power systems. Furthermore, the synchronization of networks proves instrumental in solving engineering quandaries, such as cryptography and image encryption. And finite-time synchronization (FTS) controls exhibit substantial resistance to interference, accelerating network convergence speed and heightening control efficiency. In this paper, finite-time synchronization (FTS) is investigated for a class of fractional-order nonidentical complex networks under uncertain parameters (FONCNUPs). Firstly, some new FTS criteria for FONCNUPs are proposed based on Lyapunov theory and fractional calculus theory. Then, the new controller is designed based on inequality theory. Compared to the general controller, it controls all nodes and adds additional control to some of them. When compared to other controllers, it has lower control costs and higher efficiency. Finally, a numerical example is presented to validate the effectiveness and rationality of the obtained results.

Exponential Output Synchronization of Complex Networks With Output Coupling via Intermittent Event-Triggered Control

This paper considers the exponential output synchronization of complex networks with output coupling (CNOC) based on the intermittent event-triggered control (IE-TC) strategy. Unlike existing intermittent control strategies, the proposed IE-TC strategy is event-triggered instead of time-triggered during the control intervals. Moreover, the average control rate is adopted for intermittent control, which makes the results less conservative. A new Lyapunov function is proposed to simplify the proof, which does not require the traditional mathematical induction method for intermittent control. Based on the Lyapunov method and inequality technique, sufficient conditions for achieving exponential output synchronization of CNOC for undirected graph and digraph topologies are given, respectively. Moreover, the Zeno phenomenon can be excluded. Finally, an example with simulations is provided to verify the feasibility of the theoretical results.

Quantized adaptive practical fixed-time synchronization of stochastic complex networks with actuator faults

This paper investigates the practical fixed-time synchronization for stochastic complex networks (CNs) under quantized adaptive fault-tolerant control scheme. More accurate upper-bound estimates of stochastic settling time are obtained and novel residual sets are derived via proposed new lemmas for practical fixed-time stability in probability (PFTP). Quantized adaptive control scheme is designed based on the improved lemmas, which can deal with the unknown actuator faults and disturbances in CNs. Moreover, the proposed control strategy can make the stochastic CNs achieve practical fixed-time synchronization in probability (PFSP). In addition, the effectiveness of proposed method is confirmed by an example of Chua’s circuit.

Low Energy Cost Synchronization Strategy for Markovian Switching Complex Systems/Networks: Multiple Perspectives Comparative Analysis

In this paper, the low energy cost synchronization control strategy of Markovian switching complex systems/networks is mainly studied and analyzed through multiple perspectives. Firstly, in order to achieve synchronization of Markovian switching complex networks with low energy cost, a control scheme based on the optimal node selection strategy that does not depend on the network coupling strength is improved, and a finite-time controller with a simpler structure is constructed. Secondly, based on the event-triggered control strategy an effective trigger event is designed to achieve the low energy cost synchronization of Markovian switching complex networks on the basis of reducing the information transmission and interaction between networks. Finally, the two control strategies mentioned in this paper are compared and analyzed from multiple perspectives through numerical simulations to better guide practical engineering.

Observer-based aperiodically intermittent pinning synchronization of complex-valued dynamical networks with time-varying delay

This paper addresses the impact of time delay and unavailability of system states on synchronization in complex networks. Specifically, it focuses on observer-based synchronization of complex-valued dynamical networks (CDNs) with time-varying delays, encompassing both complex-valued node dynamics and outer coupling forms. Two aperiodically intermittent control schemes, with and without pins, are proposed to reduce control costs by minimizing control frequency and the number of controllers. The proposed schemes establish sufficient criteria for guaranteeing synchronization in CDNs with time-varying delays, utilizing a combination of Lyapunov function and inequality technology in the complex field. Numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.

Finite-time lag synchronization for two-layer complex networks with impulsive effects

&lt;abstract&gt;&lt;p&gt;This paper mainly considered the finite-time lag synchronization for two-layer complex networks with impulsive effects. Different types of controllers were designed to achieve the lag synchronization of two-layer complex networks. Several sufficient conditions on lag synchronization in the sense of finite time were derived. The time for synchronization was also estimated. It is important to note that synchronization time was influenced by the initial value, as well as the impulses and impulse sequence. This implied that different impulse effects result in varying synchronization times. Additionally, desynchronizing impulses can extend the synchronization time, whereas synchronizing impulses have the opposite effect. Finally, a numerical example was presented to showcase the practicality and validity of the proposed theoretical criteria.&lt;/p&gt;&lt;/abstract&gt;

Robust [formula omitted] synchronization for parabolic complex networks with coupling time-varying delays

This paper delves into the robust H∞ synchronization for diffusion-type parabolic complex networks (PCNs) characterized by second-order nonlinear partial differential equations (PDEs). Given that the potential deterioration of network performance or the loss of network synchronization caused by external disturbances and time delays, the analysis and synthesis results for the robust H∞ synchronization of the PCNs with coupling time-varying delays are derived with and without the utilization of the distributed adaptive state feedback control protocol. A numerical example is employed to validate the effectiveness of the acquired H∞ synchronization results and the adaptive protocol.

Stability control of a two‐lane car‐following model based on cluster synchronization of complex network

AbstractThe article investigated the stability of a two‐lane car‐following model with lateral friction on the basis of cluster synchronization theory of complex network. By using the Lyapunov stability theory and designing the appropriate controller, the two‐lane car‐following model with lateral friction is quickly stabilized and the stability condition of the model is obtained. Besides, based on the adaptive cluster synchronization theory for complex networks with external disturbances, the stability of two‐lane car‐following model with lateral friction is studied when the vehicles is subjected to random external disturbance. Finally, the numerical simulation is carried out by using Matlab simulation technology, the results show that the two‐lane car‐following model with lateral friction is rapidly stabilizing and congestion phenomenon is effectively alleviated under the controller designed.

Synchronization of fractional-order fuzzy complex networks with time-varying couplings and proportional delay

The topic of synchronization of fractional-order fuzzy complex networks with time-varying couplings and proportional delay is addressed in this paper. By combining graph theory, the Lyapunov method, and the Razumikhin method, the synchronization criteria are obtained by designing a new time-varying graph-theoretical Lyapunov function. Different from the typical quadratic Lyapunov function, the time-varying graph-theoretical Lyapunov function contains the product of three-term functions and poses the difficulty of fractional derivative due to the unavailability of the general Leibniz formula and the chain rule. A new inequality about the fractional derivative rule of the time-varying graph-theoretical Lyapunov function is established based on the convex function creatively. In addition, compared with relevant literatures, the synchronization criteria are related to the proportionality coefficient and the order of fractional derivative. Then, the synchronization of fractional-order power system established on fuzzy complex networks with time-varying couplings and proportional delay is studied for the first time by applying the feedback control. Lastly, some simulations are exhibited to demonstrate the effectiveness of the theoretical results.

Particle swarm optimization based leader-follower cooperative control in multi-agent systems

Multi-agent systems (MAS) have attracted significant attention in recent years due to their wide applications in cooperative control, formation control, synchronization of complex networks, and distributed coordination. A fundamental problem in MAS is the leader-follower consensus or cooperative tracking, where the followers are required to track the state trajectory of the leader agent. To solve the leader-follower consensus problem, we propose a novel evolutionary computation approach to design the optimal distributed control protocols for leader-follower MAS. First, we formulate the design of distributed control gains for leader-follower consensus as an optimization problem to minimize tracking errors. Then, we leverage particle swarm optimization as an efficient evolutionary technique for distributed gain optimization in multi-agent networks. Finally, we guarantee stability for the closed-loop dynamics under directed communication topologies based on algebraic graph theory. The simulation results indicate that the proposed method yields a diminished tracking error, expedites the convergence process, and minimizes the requisite control effort while enhancing computational efficiency. Furthermore, these results exemplify the method's versatility when applied to nonlinear dynamic scenarios, directed network topologies, fluctuating disturbances, and optimization across multiple domains.

Event‐triggered sampled‐data synchronization of complex networks with uncertain inner coupling and time‐varying delays

AbstractThis paper focuses on event‐triggered sampled‐data synchronization of uncertain complex networks with time‐varying coupled delays. First of all, a discrete event‐triggered sampled‐data control scheme is adopted, which not only makes the state of the system be monitored in discrete time, but also the sampling information is effectively transmitted. The proposed event‐triggered mechanism effectively prevents Zeno behavior. In addition, we also use some novel piecewise time‐dependent Lyapunov–Krasovskii and Wirtinger inequality to handle the time‐varying delays and parameter uncertainties of complex networks. Then, synchronization criteria are given for uncertain complex networks. Finally, the simulation results show that the control scheme can significantly reduce the number of transmitted signals while maintaining the uncertain complex networks synchronization.

Synchronization of stochastic switching complex networks with a target of nonzero inputs

SummaryIn this article, we study the mean square synchronization problems for complex networks with a target of nonzero inputs under stochastic switching topology that is driven by an ergodic continuous‐time Markov process. First, we design an adaptive continuous controller based on relative full states that is consist of a synchronization term and an uncertainty elimination term, where the latter term can completely eliminate the effects of target's nonzero inputs and is continuous by adding an exponential decay function with positive initial values into the denominator. By developing a stochastic Lyapunov function, we show that zero error synchronization in the mean square sense can be achieved if the union of switching graphs contains a directed spanning tree with the target being the root. Second, we design an adaptive continuous controller based on relative outputs. Finally, we give two simulation examples to validate the theoretical results.