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This paper investigates the problem of fixed-time synchronization of time-varying coupled competitive neural networks with impulsive effects. Synchronizing impulses and desynchronizing impulses are each taken into account. The innovative pure power-law control is designed in this paper to avoid vibratory behaviors, which is more straightforward and effective than the common design including the linear and power-law terms. Note that the key difficulty is determining how to ensure fixed-time synchronization and estimate the settling time in an impulsive sense since the impulsive influences may lead to the discontinuity of the states. However, the theoretical framework of fixed-time synchronization under desynchronizing impulses has not been constructed much in the existing literature, which deeply motivated us to contribute to this analysis. By using the average impulsive intervals method, graph theory, and the Lyapunov method, two cases of the settling time along with the fixed-time synchronization criteria regarding the synchronizing and desynchronizing impulses are given. Lastly, a numerical example is provided to show the viability and accuracy of the discovered theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on the synchronization control problem for neural networks (NNs) subject to stochastic cyber-attacks. Firstly, an adaptive event-triggered scheme (AETS) is adopted to improve the utilization rate of network resources, and an output feedback controller is constructed for improving the performance of the system subject to the conventional deception attack and accumulated dynamic cyber-attack. Secondly, the synchronization problem of master–slave NNs is transformed into the stability analysis problem of the synchronization error system. Thirdly, by constructing a customized Lyapunov–Krasovskii functional (LKF), the adaptive event-triggered output feedback controller is designed to ensure the synchronization error system is asymptotically stable with a given H ∞ performance index. Lastly, in the simulation part, two examples, including Chua's circuit, illustrate the feasibility and universality of the related technologies in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the exponential synchronization of fractional-order multi-links complex dynamical networks (CDNs) is studied based on non-periodically intermittent control. By means of the Lyapunov method and graph-theoretic approach, a Lyapunov-type theorem is provided based on the existence of vertex-Lyapunov functions. Then by giving the specific vertex-Lyapunov functions, a coefficients-type theorem is presented where the conditions of it are based on the coefficients of system. Moreover, to show the practicality of theoretical results, we give two applications to fractional-order chaotic CDNs with multiple links and fractional-order Hindmarsh–Rose neuron systems with multiple links, respectively. Meanwhile, two numerical examples are given to demonstrate the validity and feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

The paper is devoted to investigating the quasi-synchronization issue of fractional-order multi-layer networks with mismatched parameters under delay-dependent impulsive feedback control. It is worth highlighting that fractional-order multi-layer networks with mismatched parameters, as the extension model for single-layer or two-layer ones, are constructed in this paper. Simultaneously, the intra-layer and inter-layer couplings are taken into consideration, which is more general and rarely considered in discussions of network synchronization. An extended fractional differential inequality with impulsive effects is given to establish the grounded framework and theory on the quasi-synchronization problem under delay-dependent impulsive feedback control. Moreover, in the light of the Lyapunov method and graph theory, two criteria for achieving the quasi-synchronization of fractional-order multi-layer networks with mismatched parameters are derived. Furthermore, exponential convergence rates as well as the bounds of quasi-synchronization errors are successfully deduced. Ultimately, the theoretical results are applied in a practical power system, and some illustrative examples are proposed to show the effectiveness of theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed-time bipartite synchronization issue of nonlinear impulsive time-varying signed networks with time delays. Under the average impulsive interval method, two Lyapunov lemmas are given to ensure the fixed-time stability of nonlinear impulsive time-varying systems. The new settling-time estimations are accurately calculated in terms of the influences of the stabilizing and destabilizing impulses. Furthermore, based on the proposed fixed-time stability theory and the Lyapunov functional method, some sufficient conditions are established to ensure the fixed-time bipartite synchronization of the studied signed networks, and the settling-time estimations are given respectively as well. Moreover, under our theoretical results, an application of coupled time-varying spring-mass-damper systems with impulsive effects is studied. Finally, a numerical example is provided to show the effectiveness of the main results, and the simulation results reveal that synchronizing impulses can shorten the convergence time of the system states while desynchronizing impulses can increase that. • A new theoretical framework for the fixed time stability of nonlinear impulsive time-varying systems is established. • The settling time is fully estimated in terms of stabilizing and destabilizing impulses. • An application of coupled time-varying spring-mass-damper systems with impulsive effects is provided. [ABSTRACT FROM AUTHOR]

In this paper, the issue of exponential synchronization of fractional-order multilayer coupled neural networks with reaction-diffusion terms is investigated by using periodically intermittent control. It deserves to mention that spatial diffusions, multilayer interactions and fractional dynamics are introduced to coupled neural networks at the same time. A novel fractional-order differential inequality is established on the basis of Caputo partial fractional operator. Moreover, to realize exponential synchronization of the underlying neural networks, some sufficient conditions are presented with the help of Lyapunov method and graph theory. Theoretical results show that the exponential convergence rate is dependent on the control gain and the order of fractional derivative. Finally, an illustrative numerical example is provided to further verify the feasibility and effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper discusses the adaptive event-triggered synchronization problem of a class of neural networks (NNs) with time-varying delay and actuator saturation. First, in view of the limited communication channel capacity of the network system and unnecessary data transmission in the NCSs, an adaptive event-triggered scheme (AETS) is introduced to reduce the network load and improve network utilization. Second, under the AETS, the synchronization error model of the delayed master-slave synchronization system is constructed with actuator saturation. Third, based on Lyapunov–Krasovskii functional (LKF), a new sufficient criterion to guarantee the asymptotic stability of the synchronization error system is derived. Moreover, by solving the stability criterion expressed in the form of a set of linear matrix inequalities (LMIs), some necessary parameters of the system are obtained. At last, two examples are expressed to demonstrate the feasibility of this method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, the stability and synchronization problems of fractional‐order delayed multilink complex networks with nonlinear hybrid couplings are investigated simultaneously, where discrete time‐varying delays and distributed time‐varying delays are both taken into account. By virtue of graph‐theoretic approach and Lyapunov method, under feedback control, some criteria are established to guarantee that the underlying networks achieve stability and synchronization. The obtained criteria are related to topological structure of subsystems, control gain, and the upper bound of time‐varying delays. Furthermore, in order to show practicality, the obtained results are applied to fractional‐order delayed multilink competitive neural networks with nonlinear hybrid couplings and fractional‐order Lorenz chaotic delayed coupled systems with nonlinear hybrid couplings, respectively. Finally, two numerical examples are given to illustrate the effectiveness and feasibility of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of global Mittag-Leffler synchronization of multi-links impulsive fractional-order complex networks (MIFCNs). A class of feedback control based on discrete-time state observations is first adopted for synchronization of MIFCNs. By combining Lyapunov method with graph-theoretic approach, a synchronization criterion for MIFCNs is derived. In particular, this synchronization criterion is related to the order of fractional derivatives, the parameters of control and the topological structure of networks. Furthermore, as an application of our theoretical results, synchronization of multi-links impulsive fractional-order BAM neural networks is studied in detail and a synchronization criterion is also provided. Finally, a numerical example is presented to illustrate the validity and feasibility of theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the global synchronization of fractional complex-valued neural networks with pantograph delays and inhibitory factors is investigated, and some sufficient conditions are obtained. It deserves to mention that the attained sufficient conditions show that some factors including the pantograph coefficient, coupling connection weights, inhibitory factors, and the order of fractional derivative have an influence on network synchronization. Moreover, when complex-valued neural networks degenerate into real-valued cases and inhibitory factors are not taken into consideration, they are also discussed, and two corollaries are derived. Finally, to validate the feasibility of the theoretical results, a numerical example is presented. Meanwhile, some contrastive numerical results are given to illustrate the relationships among network synchronization, pantograph coefficient, and inhibitory factors. [ABSTRACT FROM AUTHOR]

In this paper, the issue of finite-time lag synchronization of coupled reaction–diffusion systems with time-varying delay (CRDSTD) is considered. A periodically intermittent controller is designed such that drive system and corresponding response system can achieve finite-time lag synchronization. By using graph theory and Lyapunov method, two sufficient criteria are presented to guarantee the finite-time lag synchronization of CRDSTD. Moreover, the time of achieving lag synchronization of CRDSTD is estimated. Finally, a numerical example is given to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper concentrates on the global synchronization of the fractional‐order multi‐linked complex network (FMCN) via periodically intermittent control. It should be stressed that periodically intermittent control is employed to the FMCN for the first time. Moreover, the network is defined on digraphs with different weights, and two situations on topological structure of the network are discussed, including each digraph being strongly connected, and the biggest one being strongly connected. Based on Lyapunov method and graph theory, some synchronization criteria are obtained under two situations. And, the obtained synchronization criteria have a close relationship with the order of fractional‐order derivative, coupling strength, control gain, control rate, and control period. Besides, for practicability, theoretical results are applied to studying the synchronization of fractional‐order multi‐linked chaotic systems, and some sufficient conditions are provided. For a special case, fractional‐order multi‐linked Lorenz chaotic systems, numerical simulations are given to indicate the feasibility of theoretical results and the effectiveness of control strategy. [ABSTRACT FROM AUTHOR]

In this paper, finite-time inner synchronization of coupled systems on a network with time delay and distributed delay (CSNTD) is investigated. And here, time delay and distributed delay are both taken into consideration when modelling a realistic network. Different from common feedback control, the controller we design is quantized, which is more realistic and reasonable. By using Lyapunov method and Kirchhoff’s Matrix Tree Theorem, some sufficient criteria are derived to guarantee finite-time inner synchronization of CSNTD. It should be underlined that the method is first applied to studying the issue of finite-time inner synchronization of CSNTD and the synchronization time we obtain has a close relationship with the topological structure of the network. Moreover, to verify our theoretical results, we present an application to coupled oscillators with time delay and distributed delay, and a sufficient criterion is obtained. Ultimately, a numerical example is given to verify the validity and feasibility of theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, instead of separating the complex-valued system into two real-valued systems, the finite-time synchronization of fractional-order complex-valued coupled systems is investigated for the first time. Compared with other finite-time synchronization control, it should be stressed that an effective and novel controller is firstly designed without the help of sign functions. Moreover, some sufficient conditions are derived on the basis of the graph-theoretic approach and the theory of complex functions. Besides, the settling time of synchronization is estimated which is related to the order of fractional derivative, control parameters and the topological structure of the networks. Finally, two numerical examples are provided to show the feasibility and effectiveness of theoretical results. • Finite-time synchronization of fractional-order complex coupled systems is studied. • An effective control strategy is adopted to realize finite-time synchronization. • This paper is based on graph-theoretic approach and the theory of complex functions. • Some easy verified algebraic conditions are derived without separation method. [ABSTRACT FROM AUTHOR]

In this article, we analyze the asymptotic synchronization of fractional-order multiplex networks with time delays via adaptive control, where intra-layer and inter-layer transmission delays are taken into consideration. By introducing a new fractional-order Halanay-type inequality and utilizing graph-theoretic method and Lyapunov method, we formulate some sufficient conditions to ensure the asymptotic synchronization of fractional-order multiplex networks with time delays. Furthermore, in the case that there is no delay in intra-layer and inter-layer transmissions, we investigate the finite-time synchronization of fractional-order multiplex networks by impulsive control. Meanwhile, the upper bound of the settling time for finite-time synchronization is reckoned. In addition, the results herein are applied to coupled Chua's circuits on fractional-order multiplex networks with time delays. Finally, some numerical simulations are carried out to demonstrate the effectiveness of the developed results. [ABSTRACT FROM AUTHOR]