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Considering the media coverage and age‐dependent education, a deterministic and a stochastic class‐age‐structured rumor propagation models are studied, respectively. First, the deterministic rumor propagation model is characterized by a coupled system of ordinary and partial differential equations. The positivity and boundness of solutions are proved, and the basic reproduction number is derived. Second, the stochastic rumor propagation model is formulated by stochastic differential equations. The existence of global positive solutions in model is discussed with the Itô's formula and stochastic Lyapunov function. Additionally, by utilizing comparison principle of stochastic differential equations and the strong law of large numbers, several sufficient conditions for extinction and persistence of the rumor are derived. Finally, numerical simulations are carried out for illustrating the results. [ABSTRACT FROM AUTHOR]

This article considers the fixed‐time distributed optimization problem of multi‐agent systems with external disturbances, in which the global optimization objective is a convex combination of local objective functions. To solve this issue, a directed communication network is carefully designed, and an integral sliding mode control protocol is proposed based on the gradient of global objective function first. Moreover, two distributed optimal protocols are designed by using the gradient and the Hessian matrix of local objective function, respectively. By employing Lyapunov stability theory, graph theory, convex analysis, and inequality techniques, we prove that all proposed protocols can make agents achieve consensus and converge accurately to the optimal solution of the considered problem in some fixed‐time intervals. Finally, some numerical simulations are given to verify the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the problems of quasi‐projective synchronization (QPS) and finite‐time synchronization (FTS) for a kind of delayed fractional‐order BAM neural networks (DFOBAMNNs). In order to reach the goals of synchronization and more accurately gauge of settling time and error level, several fresh quantized controllers are structured to make the utmost of confined communication resources. Then, based on the finite‐time theorem, quantized control strategy, Lyapunov function theory and properties of Mittag–Leffler function as well as inequality analysis techniques, some plentiful criteria are formed to set up a relation between control gains and quantization parameters. In addition, the corresponding error bound of QPS and guages of the settling time on FTS are also given. Finally, a few numerical examples are introduced to validate the effectiveness of the presented control protocols. [ABSTRACT FROM AUTHOR]

This article considers the consensus of multi‐agent systems (MASs) with external disturbances by using sliding mode control. First, by establishing a novel sliding mode surface and designing a sliding mode control protocol with constant gains, the consensus of MASs with unknown bounded disturbances is studied. Second, based on the barrier function, a new type of adaptive sliding mode switching protocol is proposed, in which the control gains can be chosen randomly and the upper bound of the disturbance does not need to be known in a prior. By using this protocol, the consensus error can converge to any given region of zero in finite time. Moreover, the leaderless consensus and leader‐following tracking problem of MASs with general dynamics and external disturbances are also investigated via extending the proposed adaptive sliding mode protocol. Finally, some examples are presented to illustrate the effectiveness of the control strategies. [ABSTRACT FROM AUTHOR]

In this article, we considered the fixed‐time stability (FXT) of a type of discontinuous dynamical system. First, we introduced some new FXT stability results via variable substitutions and using inequality techniques, which are more accurately estimate the upper bound of settling time (ST). Then, based on the established results and using the differential inclusion theory, we investigated the FXT synchronization of a type of general neural networks (NNs) with state‐dependent switching coefficients and discontinuous neuron activation functions via introducing a type of discontinuous controller which is more simple compared to existing results. In addition, the estimated upper bound of ST shown to be independent to the initial values of considered drive‐response networks, and it is much smaller and nearer to the real synchronization time than those given in the previously published works. Lastly, two numerical examples are given to demonstrate the feasibility of our derived theoretical results. We believe that the results of this article can give some new insights for the FXT stabilization and FXT synchronization analysis of state‐dependent switching dynamics with or without discontinuous right‐hand sides. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the problem of pinning synchronization for delayed complex directed networks via generalized intermittent adaptive control strategy is considered. First, a dynamical mode of delayed network is investigated. Second, a generalized intermittent adaptive control strategy which unified the traditional periodic intermittent control and the aperiodic case is introduced. Additionally, by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria to ensure the global synchronization of delayed complex networks based on the designed control protocols are obtained. Finally, an example with numerical simulations is provided to demonstrate the validness of the theoretical results proposed scheme. [ABSTRACT FROM AUTHOR]

Summary: This study is mainly concerned with the general decay synchronization (GDS) problem of a class of inertial neural networks (INNs) with time‐varying delay. First, unlike the methods used in previous relevant literature where both of the master and slave systems were transferred into the first‐order differential equations, only error dynamical system is transferred into the reduced‐order differential equation. Then, by designing a novel nonlinear output feedback controller and constructing suitable Lyapunov functionals, some simple and useful sufficient conditions ensuring the GDS of considered INNs are established via employing useful analysis techniques and linear matrix inequality approach. In addition, two examples are presented to show the effectiveness of the established theoretical results. [ABSTRACT FROM AUTHOR]

Summary: The dissipativity of discrete‐time switched memristive neural networks with actuator saturation is considered in this paper. By constructing a quasi‐time‐dependent Lyapunov function, sufficient conditions are obtained to guarantee the exponential stability and exponential dissipativity for the closed‐loop system with mode‐dependent average dwell time switching. Furthermore, the exponential H∞ performance of discrete‐time switched memristive neural networks is also analyzed, while the quasi‐time‐dependent controller and observer gains of the desired exponential dissipative and H∞ performance can be calculated from linear matrix inequalities. Finally, the effectiveness of theoretical results is illustrated through the numerical examples. [ABSTRACT FROM AUTHOR]

The leader‐following guaranteed‐performance consensus problems for second‐order multi‐agent systems with and without communication time delays are investigated, where a guaranteed performance function is proposed to consider the consensus regulation performance. For the case without the time delay, the coupling gain and pinning strength are carefully considered. When the time delays exist in the communication, we find that the inequality (Seuret and Gouaisbaut) cannot be used to investigate the consensus problems proposed in the study since the obtained conditions cannot be satisfied. Therefore, Jensen's inequality and Newton–Leibniz formula, which can solve this issue well, are introduced. By using the state space decomposition approach, linear matrix inequality and Lyapunov stability theory, some sufficient conditions are derived for achieving the guaranteed performance consensus. Moreover, the upper bound of the performance function is determined. Finally, two examples are shown to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

Summary: The H∞ control problem for memristive neural networks with aperiodic sampling and actuator saturation is considered in this paper. A novel approach that is combined with the discrete‐time Lyapunov theorem and sampled‐data system is proposed to cope with the aperiodic sampling problem. On the basis of such method and choosing a polyhedral set, sufficient conditions to determine the ellipsoidal region of asymptotic stability and exponential stability for the estimation error system are obtained through a saturating sampled‐data control. Furthermore, H∞ performance index of memristive neural networks with disturbance is also analyzed, whereas the observer and controller gains are calculated from stability conditions of linear matrix inequalities. Finally, the effectiveness of the theoretical results is illustrated through the numerical examples. [ABSTRACT FROM AUTHOR]

This paper discusses the consensus problem of second-order multiagent systems with nonlinear dynamics. A directed spanning tree--based adaptive control protocol is developed, which overcomes the drawback that the spectrum of the Laplacian matrix must be known a priori. A scheme for reordering the nodes is proposed. Applying the developed method and the Lyapunov stability theory, some distributed adaptive laws are designed in the directed network. It is found that the consensus can be achieved by randomly choosing a directed spanning tree and using the developed distributed adaptive law. Finally, an example is presented to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we concern the exponential synchronization problem for hybrid-coupled delayed dynamical networks via aperiodically intermittent control. Different from previous works, the delayed coupling term considered here contains the transmission delay and self-feedback delay, and the intermittent control can be aperiodic. By utilizing a different technique compared with some previous results, several useful criteria are derived analytically to realise exponential synchronization for a class of coupled complex network. As a special case, some sufficient conditions ensuring the exponential synchronization for a class of coupled neural network are obtained. Finally, a numerical example is given to demonstrate the validness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, a discrete Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model with standard incidence rate is studied. By means of the iteration technique and the comparison principle of difference equations, the sufficient conditions are obtained for the global attractivity of the endemic equilibrium when the basic reproduction number [ABSTRACT FROM AUTHOR]