Synchronization Of Stochastic Complex Networks Research Articles

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.

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.

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.

Pinning Synchronization for Stochastic Complex Networks With Randomly Occurring Nonlinearities: Tackling Bit Rate Constraints and Allocations.

In this article, the ultimately bounded synchronization problem is investigated for a class of discrete-time stochastic complex networks under the pinning control strategy. Communication between system nodes and the remote controller is facilitated via wireless networks subject to bit rate constraints. The system model is distinguished by the inclusion of randomly occurring nonlinearities. A coding-decoding transmission mechanism under constrained bit rates is introduced to characterize the digital transmission process. To achieve synchronization of the network nodes with the unforced target node, a pinning controller is specifically devised based on the information from partially selected nodes. Through the application of the stochastic analysis method, a sufficient condition is derived for ensuring the mean-square boundedness of the synchronization error system. In addition, an optimization algorithm is introduced to address bit rate allocation and the design of desired controller gains. Within the presented theoretical framework, the correlation between the mean-square synchronization performance and bit rate allocation is further elucidated. To conclude, a simulation example is provided to substantiate the efficacy of the recommended pinning control approach.

Prescribed-Time Synchronization of Stochastic Complex Networks With High-Gain Coupling

Prescribed-Time Synchronization of Stochastic Complex Networks With High-Gain Coupling

Event-triggered delayed impulsive control for synchronization of stochastic complex networks under deception attacks

This paper analyzes a class of stochastic complex networks (SCNs) subjected to deception attacks via the event- triggered delayed impulsive control (ETDIC) strategy. Noting the universality of delay, we consider the delay in impulsive control. The impulse is combined with the event-triggered mechanism (ETM), that is, the impulsive instant is determined by the ETM, which is defined by the network topology and the Lyapunov function. Based on this ETM, through a combination of the Lipschitz-Razumikhin method and graph theory, we obtain the conditions to avoid Zeno behavior and give some criteria of pth moment exponential synchronization (PMES) for SCNs under deception attacks. The criteria are related to the topology of the network, the event-triggered parameters, and the attack signals sent by the enemy. Finally, we analyze a class of coupling Chua’s circuits subjected to deception attacks and present numerical examples to verify the validity and practicability of our theoretical results.

Adaptive Finite-time Synchronization of Stochastic Complex Networks with Mixed Delays via Aperiodically Intermittent Control

Adaptive Finite-time Synchronization of Stochastic Complex Networks with Mixed Delays via Aperiodically Intermittent Control

Synchronization of stochastic complex networks with time-delayed coupling

Noise and time delay are inevitable in real-world networks. In this article, the framework of master stability function is generalized to stochastic complex networks with time-delayed coupling. The focus is on the effects of noise, time delay, and their inner interactions on the network synchronization. It is found that when there exists time-delayed coupling in the network and noise diffuses through all state variables of nodes, appropriately increasing the noise intensity can effectively improve the network synchronizability; otherwise, noise can be either beneficial or harmful. For stochastic networks, large time delays will lead to desynchronization. These findings provide valuable references for designing optimal complex networks in practical applications.

Finite-time pinning impulsive synchronization of stochastic complex networks with mixed delays

This paper mainly considers the finite-time synchronization (FTS) of stochastic complex networks with mixed delays via pinning impulsive control. Firstly, a novel pinning impulsive controller is introduced by selecting the nodes of the stochastic complex network with large error norms, which not only saves control resources, but also ensures that stochastic complex network with mixed delays can realize FTS. It is worth noting that the finite-time control strategy constructed is not affected by the sign function. Secondly, a uniform FTS criterion under synchronizing impulses and desynchronizing impulses is derived based on the idea of average impulsive interval. Moreover, the obtained sufficient condition are further extended to general stochastic complex networks and stochastic complex networks with mixed delays under delayed impulses. Finally, the feasibility of the theory results is verified by a numerical example.

Stochastic Synchronization of Nonlinear Networks With Directed Graphs and Degenerate Noise

Noise is ubiquitous in network systems and has profound impacts on network dynamics. Despite substantial progress in stochastic synchronization of complex networks, most studies limit their focus to nondegenerate noise. However, the influence of degenerate noise on synchronization has not been studied properly. Here, we tackle this challenging problem by introducing a network of nonlinear units with a deterministic communication digraph and a noisy communication digraph. The communication links in the noisy communication digraph are affected by degenerate noise in a relative-dependent manner. Two types of deterministic communication digraphs are considered: 1) the case of strongly connected graphs and 2) the case of graphs containing a spanning tree. By using the algebraic graph theory and the stability theory of stochastic differential equations, algebraic sufficient conditions for both cases are derived, which depend on node dynamics, network structure, and coupling strengths. These criteria demonstrate that strong deterministic communication can compensate for the detrimental effect of degenerate noise, thus ensuring the stochastic synchronization in the almost sure sense. Numerical simulations support and illustrate the proposed theoretical results.

Fixed-time synchronization of stochastic complex networks with mixed delays via intermittent control

This paper studies the problem of fixed-time synchronization in stochastic complex networks. Through the intermittent control strategy, a new controller is designed, so that the system is not affected by the initial value and achieves synchronization at a fixed-time. The controller avoids the influence brought by the sign function and also suitable for directed networks. Establish sufficient conditions for Lyapunov function to derive synchronization. Finally, a simulation example verifies the effectiveness of the proposed method and compares it with the finite-time synchronization.

Estimation of the time cost with pinning control for stochastic complex networks

&lt;abstract&gt;&lt;p&gt;In this paper, the finite-time and fixed-time stochastic synchronization of complex networks with pinning control are investigated. Considering the time and energy cost of control, combining the advantages of finite-time control technology and pinning control technology, efficient protocols are proposed. Compared with the existing research, the influence of noise is considered, and sufficient conditions for the network to achieve stochastic synchronization in a finite time are given in this paper. Based on the stability theory of stochastic differential equations, the upper bound of the setting time is estimated. Finally, the effects of control parameters, noise intensity, and the number of control agents on the network synchronization rate are studied. Numerical simulations verify the validity and correctness of the theoretical results.&lt;/p&gt;&lt;/abstract&gt;

Fixed‐time synchronization of stochastic complex networks with Markov jump and mixed delays via adaptive non‐chattering control

AbstractIn this article, the fixed‐time synchronization problem for stochastic complex networks (CNs) with Markov jump and mixed delays is investigated. Compared with fixed‐time synchronization of stochastic CNs in existing literature, the fixed‐time synchronization for stochastic CNs with Markov jump and mixed delays is studied for the first time, which is of better significance. Utilizing the Lyapunov method, under the framework of adaptive non‐chattering control, some fixed‐time synchronization conditions are derived. Besides, from the results of the convergence time, the convergence time obtained by the fixed‐time synchronization studied in this article does not depend on the initial value of the system, but is only related to the control parameters. Eventually, a numerical example is also carried out to demonstrate the practicability and validity of our proposed results. Furthermore, a secure communication synchronization problem is presented to illustrate the effectiveness of the obtained results.

Fixed-time and preassigned-time stochastic synchronization of complex networks via quantized event-triggered strategy

Fixed-time and preassigned-time stochastic synchronization of complex networks via quantized event-triggered strategy

Improved results on synchronization of stochastic delayed networks under aperiodically intermittent control

This paper addresses the synchronization of stochastic complex networks with time-varying delay via aperiodically intermittent control (AIC). By proposing the concepts of average control ratio and average control frequency for AIC, some new synchronization conditions are obtained, which relax the constraints of the lower bound of control widths and the upper bound of control periods. And the proportion of rest widths can be any value in (0,1). So the constraints on AIC are loosened and thus the conservativeness is reduced compared with the existing related results. Two types of time delay are investigated: (i) the upper bound of time-varying delay should be smaller than the average control width but can be larger than the lower bound of control widths; (ii) the upper bound of time-varying delay has no relationship with control and rest widths. An example of coupled stochastic oscillators systems is presented to show the effectiveness and superiority of our results.

Distributed Synchronization of Stochastic Complex Networks with Time-Varying Delays via Randomly Occurring Control

This paper studies the distributed synchronization control problem of a class of stochastic dynamical systems with time-varying delays and random noise via randomly occurring control. The activation of the distributed adaptive controller and the update of the control gain designed in this paper all happen randomly. Based on the Lyapunov stability theory, LaSalle invariance principle, combined with the use of the properties of the matrix Kronecker product, stochastic differential equation theory and other related tools, by constructing the appropriate Lyapunov functional, the criterion for the distributed synchronization of this type of stochastic complex networks in mean square is obtained.

Finite-time synchronization of stochastic complex networks with random coupling delay via quantized aperiodically intermittent control

This paper studies the finite-time synchronization issue of stochastic complex networks (SCNs) with random coupling delay and nonlinear coupling function. Internal delay, perturbation delay are also considered into this model. Meanwhile, a quantized aperiodically intermittent control strategy is proposed to realize finite-time synchronization of SCNs. By means of Lyapunov stability theory and graph theory, two types of sufficient conditions are derived to ensure finite-time synchronization of SCNs. The obtained results are closely related to the maximum proportion of rest width and the topological structure of considered networks. Moreover, the theoretical results is applied to study finite-time synchronization of stochastic coupled oscillators. Finally, a numerical example is presented to demonstrate the effectiveness and feasibility of the obtained results.

Cluster stochastic synchronization of complex dynamical networks via fixed-time control scheme

By means of fixed-time (FDT) control technique, cluster stochastic synchronization of complex networks (CNs) is investigated. Quantized controller is designed to realize the synchronization of CNs within a settling time. FDT synchronization criteria are established with the help of Lyapunov functional and comparison system methods. It should be noted that the convergence of synchronization is further improved by comparing with existing FDT synchronization results. Numerical simulations are given to illustrate our results.

Periodically intermittent discrete observation control for synchronization of the general stochastic complex network

In this paper, the exponential synchronization of stochastic complex networks without strong connectivity is discussed. Distinguished from the previous papers, we introduce a novel periodically intermittent control based on discrete-time state observations, instead of continuous-time state observations in the control time. The coupling structure of networks is time-varying. By employing the Kirchhoff’s Matrix Tree Theorem in graph theory and Tarjan’s algorithm, some sufficient conditions are derived. In particular, when the novel control degenerates into the feedback control based on discrete-time state observations, it is discussed in detail as well. Furthermore, we apply our main results to study the synchronization of stochastic coupled oscillators with time-varying coupling structure. Meanwhile, two synchronization criteria are derived. Finally, a numerical test is given to validate the effectiveness of our results.

Exponential synchronization of stochastic complex networks with multi-weights: A graph-theoretic approach

This paper concerns the exponential synchronization problem of stochastic complex networks with multiple weights (SCNMW). By the method of network split, SCNMW can be modelled as stochastic coupled systems driven by Brownian motion. By combining graph theory, Lyapunov stability theory and state feedback control technique, drive-response synchronization criteria of SCNMW have been obtained. Two kinds of exponential synchronization criteria are obtained, one is given with Lyapunov functions of vertex systems, and the other is shown with the coefficients of SCNMW. The obtained synchronization principles are closely related to the coupling strength of multiple sub-networks and the intensity of noise perturbation. Finally, a numerical example with some simulations is presented to illustrate the theoretical results.