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With the development of the Internet, it is more convenient for people to obtain information, which also facilitates the spread of rumors. It is imperative to study the mechanisms of rumor transmission to control the spread of rumors. The process of rumor propagation is often affected by the interaction of multiple nodes. To reflect higher-order interactions in rumor-spreading, hypergraph theories are introduced in a Hyper-ILSR (Hyper-Ignorant–Lurker–Spreader–Recover) rumor-spreading model with saturation incidence rate in this study. Firstly, the definition of hypergraph and hyperdegree is introduced to explain the construction of the model. Secondly, the existence of the threshold and equilibrium of the Hyper-ILSR model is revealed by discussing the model, which is used to judge the final state of rumor propagation. Next, the stability of equilibrium is studied by Lyapunov functions. Moreover, optimal control is put forward to suppress rumor propagation. Finally, the differences between the Hyper-ILSR model and the general ILSR model are shown in numerical simulations. [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]

Due to the widespread presence of disturbances in practical engineering and widespread applications of high-order systems, this paper first pays attention to a class of high-order strict-feedback nonlinear systems subject to bounded disturbance and investigates the prescribed performance tracking control and anti-disturbance control problems. A novel composite control protocol using the technique of a disturbance observer—prescribed performance control—is designed using the back-stepping method. The disturbance observer is introduced for estimating and compensating for unknown disturbances in each step, and the prescribed performance specifications guarantee both transient and steady-state performance of the tracking error to improve the control performance and result in better disturbance rejection. Moreover, the technique of adding a power integrator is modified to tackle controller design problems for the high-order systems. The Lyapunov function method is utilized for rigorous stability analysis. It is revealed that while the control performance completely remains in the prescribed bound, all states in the closed-loop system are input-to-state stable, and the tracking error and the disturbances estimating error asymptotically converge to zero simultaneously. Then, the feasibility and effectiveness of the proposed control protocol are verified by a simulation result. [ABSTRACT FROM AUTHOR]

In this paper, synchronization analysis and parameters identification issues are explored for uncertain delayed fractional-order BAM neural networks. By designing pertinent state feedback control strategies and parameters updated laws, some ample criteria are procured for ensuring the finite-time synchronization and the Mittag-Leffler synchronization of the considered networks via exploiting the Lyapunov function theory, fractional calculus theory and inequality analysis techniques, meanwhile, the settling time of finite-time synchronization is given, which relates to the initial values. Moreover, parameters identification is actualized triumphantly for uncertain or unknown parameters. Finally, numerical examples are provided to show the availability of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates quasi-synchronization (QS) and complete synchronization(CS) for fractional-order fuzzy bidirectional associative memory neural networks. To realize QS and CS, two kinds of novel nonlinear controllers are designed, which are more general and effective compared to the existing results. By using Lyapunov function method, fractional calculation and some inequality techniques, some sufficient synchronization criteria are derived for the considered networks. Moreover, the error level of QS is estimated. Finally, two illustrative examples are presented to show the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of the finite-time synchronization is addressed for a kind of fractional-order memristive neural networks (FMNNs). First, a new power law inequality with fractional-order and two finite-time fractional differential inequalities are established by means of L’Hospital rule, Laplace transform, and reduction to absurdity, which greatly extend some existing results. In addition, unlike the traditional maximum absolute value-based method to propose memristive synaptic weights, by introducing some transformations, FMNNs are translated to a type of fractional-order systems with uncertain parameters. Furthermore, the finite-time synchronization of FMNNs is investigated by designing a discontinuous control scheme and several criteria are derived based on the developed fractional inequalities and M-matrix theory. Note that in addition to the traditional Lyapunov function with absolute value form, a more general Lyapunov function is constructed to deal with the finite-time synchronization, which makes the derived criteria more flexible and less conservative. Lastly, the derived theoretical results are verified via numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, the fixed-time lag synchronization for a general class of memristor-based neural networks (MNNs) with time delays is considered. Under the extended Filippov-framework theory, some sufficient criteria for fixed-time lag synchronization of delayed MNNs are derived based on the Lyapunov function. Besides, two types of controllers are given to ensure the fixed-time lag synchronization of the corresponding system, while the settling time of synchronization are also estimated. Finally, a numerical example is given to demonstrate the effectiveness of the developed method and the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, without dividing a complex-valued neural network into two real-valued subsystems, the global synchronization of fractional-order complex-valued neural networks (FOCVNNs) is investigated by the Lyapunov direct method rather than the real decomposition method. It is worth mentioning that the partial adaptive control and partial linear feedback control schemes are introduced, by constructing suitable Lyapunov functions, some improved synchronization criteria are derived with the help of fractional differential inequalities and L'Hospital rule as well as some complex analysis techniques. Finally, simulation results are given to demonstrate the validity and feasibility of our theoretical analysis. [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]

In this paper, the observer-based leader-following consensus problem for multi-agent systems with input saturation is studied under fixed and switching topology. Firstly, based on the measurable output information of systems, we construct an auxiliary observation system to estimate the real state information of systems. At the same time, the centralized event-triggered control is considered in the fixed and switching topology, and the Lyapunov function and Cauchy's convergence criterion are used to prove that the consensus of systems can be achieved. Secondly, the sufficient conditions of the event-triggered function are given, and it is proved that the constructed centralized event-triggered function can exclude the Zeno behavior. Then, the group case is considered in the fixed topology, and it is emphasized that the group event-triggered mechanism has the idea of event-triggered and decentralized control. Finally, the validity and feasibility of the theoretical results are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the problem of the finite-time synchronization (FTS) is studied for a class of delay neural networks (DNNs) via aperiodically intermittent control. Based on the finite-time stability theory, several new conditions ensuring FTS of two DNNs are derived by establishing a very useful differential inequality and constructing a new Lyapunov function. In addition, the proposed results here are easy to verify and they also extend the previous publications. And, the upper bounds of the settling time for synchronization are estimated. Finally, numerical simulations show the effectiveness of the derived results and the developed method. [ABSTRACT FROM AUTHOR]

In this paper, the synchronization of a class of improved neural networks with variable time delay is concerned via intermittent control. Firstly, a class of modified delayed neural networks is introduced, in which communication delays between different neurons are considered and the intra-neuron delays are negligible. Secondly, using Lyapunov functional theory, inequality techniques, and multi-parameter method, the synchronization criteria are established based on p-norm via intermittent control, and a feasible synchronization control region is given. Besides, by means of the component analysis method, the reduction to absurdity, mathematical induction, the exponential synchronization of the addressed networks is discussed in terms of the infinite norm, some criteria and the feasible control region of synchronization are also derived. Finally, some numerical examples are provided to show the validity and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global asymptotic stability and global robust stability of inertial neural networks with proportional delays. First, by using linear matrix inequality and constructing appropriate Lyapunov functional, several sufficient conditions are obtained for the global asymptotic stability of inertial neural networks with proportional delays. Furthermore, the problem of global robust stability of the network under the assumptions that the network parameters are uncertain and bounded is studied. Finally, some simulation examples are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The stability of discrete-time impulsive delay neural networks with and without uncertainty is investigated. First, by using Razumikhin-type theorem, a new less conservative condition for the exponential stability of discrete-time neural network with delay and impulse is proposed. Moreover, some new sufficient conditions are derived to guarantee the stability of uncertain discrete-time neural network with delay and impulse by using Lyapunov function and linear matrix inequality (LMI). Finally, several examples with numerical simulation are presented to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

The leader-following consensus problem of fractional-order multi-agent systems is considered. In the system, the dynamics of each agent and leader are nonlinear systems. The control of each agent using local information is designed and detailed analysis of the leader-following consensus is presented. The design technique is based on algebraic graph theory and Lyapunov method. Several simulation examples are presented as a proof of concept. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and global exponential stability of the anti-periodic solution for delayed Cohen–Grossberg neural networks with impulsive effects. First, based on the Lyapunov functional theory and by applying inequality technique, we give some new and useful sufficient conditions to ensure existence and exponential stability of the anti-periodic solutions. Then, we present an example with numerical simulations to illustrate our results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the exponential synchronization for a class of delayed recurrent neural networks is investigated by virtue of intermittent control schemes. Based on p-norm and , respectively, several new and useful synchronization criteria are derived by applying Lyapunov functional theory, mathematical induction and inequality technique. Particularly, some feasible regions of control parameters for each neuron are derived for the realization of exponential synchronization, which provides great convenience to the applications of the theoretical results. Finally, some numerical simulations are given to demonstrate the effectiveness of the proposed control methods. [Copyright &y& Elsevier]

Abstract: The global exponential synchronization for a class of fuzzy cellular neural networks with delays and reaction–diffusion terms is discussed. Some new sufficient conditions are obtained by using the Lyapunov functional method, many real parameters and inequality techniques. The result is also easy to check and plays an important role in the design and application of globally exponentially synchronization. Finally, an example is given to verify our results. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate robust stochastic stability of Markovian switching genetic regulatory networks with discrete and distributed delays. Different from previous correspondingly works, discrete and distributed delays are involved to describe the concentration of macromolecule for genetic networks. Based on the Lyapunov stability theory and linear matrix inequality (LMI), sufficient conditions are given to ensure the stability in the mean square of the stochastic genetic networks with Markovian switching. An illustrative example is given to show the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the boundedness and exponential stability for nonautonomous fuzzy cellular neural networks (FCNNs) with distributed delays and reaction–diffusion terms are investigated. By constructing suitable Lyapunov functional, introducing ingeniously some real parameters and applying the elementary inequality, we establish a series of criteria on the boundedness and globally exponential stability of solutions. In these criteria, we do not require that the response functions are bounded and differentiable. Finally, an example is given to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the uniformly boundedness and uniformly ultimately boundedness of high-order neural networks with time-varying delays are studied. Proper Lyapunov functionals and some analytic techniques are employed to derive the sufficient conditions under which the networks proposed are uniformly bounded and uniformly ultimately bounded. The results are shown to improve the results derived in (Arik, 2004). Some examples are given to illustrate the correctness of our results. [ABSTRACT FROM AUTHOR]

Abstract: By using the continuation theorem of coincidence degree theory and constructing a suitable Lyapunov functional, we derive some sufficient conditions for the existence and global exponential stability of a unique periodic solution of BAM neural networks, which assumes neither the monotony nor the boundedness of the activation functions. It is believed that these results are significant and useful for the design and applications of BAM neural networks. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the cellular neural networks with variable coefficients and infinite distributed delays. By introducing the phase space and applying Lyapunov functional method and Young inequality technique, we first establish a series of criteria on the boundedness, globally asymptotic stability and globally exponential stability. Furthermore, by applying these results and combining the existence theorems of periodic solutions for general functional differential equations with infinite delays, we establish the existence of periodic solutions and its globally asymptotic stability and globally exponential stability for the periodic cellular neural networks with infinite distributed delays. At last, as a special case, we apply these results to the autonomous cellular neural networks with infinite distributed delays and the existence, uniqueness and global stability of equilibrium point are established. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the fuzzy cellular neural networks (FCNNs) with variable coefficients and time-varying delays. A series of simple sufficient conditions is obtained for checking the boundedness, global exponential stability and the existence and global exponential stability of periodic solutions of FCNNs with variable coefficients and time-varying delays by using Young inequality and general Lyapunov functional. The results given in this paper extend and improve the earlier publications. [Copyright &y& Elsevier]

Abstract: In this Letter, based on the Lyapunov stability theorem as well as some facts about the positive definiteness and inequality of matrices, a new sufficient condition to ensure the global exponential stability of equilibrium point for autonomous delayed CNNs is obtained. This condition is less restrictive than given in the earlier references. [Copyright &y& Elsevier]

Abstract: In this Letter, we consider the recurrent neural networks with varying-time coefficients and delays. By constructing new Lyapunov functional, introducing ingeniously many real parameters and applying the technique of Young inequality, we establish a series of criteria on the boundedness, global exponential stability and the existence of periodic solutions. In these criteria, we do not require that the response functions are differentiable, bounded and monotone nondecreasing. Some previous works are improved and extended. [Copyright &y& Elsevier]

In this paper, a class of cellular neural networks with time-varying coefficients and delays is considered. By constructing a suitable Liapunov functional and utilizing the technique of matrix analysis, some new sufficient conditions on the global exponential stability of solutions are obtained. The results obtained in this paper improve and extend some of the previous results. [Copyright &y& Elsevier]

Noting that the gap between individual communication abilities is amplified in the network era, we classify spreaders into super-spreaders and ordinary spreaders by the Pareto principle. In addition, when facing negative information, individuals with higher knowledge levels will recognize it. Based on these, in this study, an improved Ignorants-Hesitant-Super-spreaders-Ordinary spreaders-Wise-Removers (IEASWR) information propagation model was developed. Meanwhile, in view of the gradual saturation, density dependence and nonlinear relationship of the propagation process, the Holling-type II functional response function is introduced to information propagation modeling for the first time making it more realistic. First, the basic reproduction number ℛ 0 is deduced. Then, the global asymptotic stability of the information-free/prevailing equilibria is proved by constructing the Lyapunov function. Furthermore, using the Pontryagin maximum principle, a real-time optimization guidance measure is proposed to achieve the correct guidance of negative information within the expected time. Finally, the validity of the theory is verified through numerical simulation. [ABSTRACT FROM AUTHOR]

This paper is concerned with complete synchronization for discrete-time fractional-order fuzzy neural networks (DFFNNs) with time-varying delays. First, three original equalities and two Caputo σ -difference inequalities are established based on theory of discrete-time fractional Calculus. Next, a novel discrete-time adaptive controller with time-varying delay is designed, by virtue of 1-norm Lyapunov function and newly established lemmas herein as well as inequality techniques and contradiction method, some judgement conditions are derived to guarantee complete synchronization for the explored DFFNNs. Benefitting from discrete-time adaptive control strategy and our analysis method, the conservatism of the derived synchronization criteria is reduced. Ultimately, the effectiveness of our theoretical results and secure communication scheme are demonstrated through two numerical examples. • We establish three original equalities, which enrich theory of discrete-time fractional Calculus. • Two Caputo σ -difference inequalities are introduced and proved herein. The first one is b c ∇ σ μ (f (t) − ϱ) 2 ⩽ 2 (f (t) − ϱ) b c ∇ σ μ f (t) , which can be applied to adaptive control-based asymptotic synchronization of nonlinear systems depicted by Caputo σ -difference equations. The second inequality is b c ∇ σ μ | f (t) | ⩽ s i g n (f (t)) b c ∇ σ μ f (t) , which plays a central role in building the relationship between 1-norm Lyapunov function and Caputo σ -difference of state variable. • A universal theoretical framework analyzing adaptive control-based complete synchronization for DFNNs is developed for the first time. • Our results are more general, which can be extended to DFNNs without fuzzy logic or DFNNs without delay. • A secure communication scheme for DFFNNTDs is proposed based on complete synchronization method. [ABSTRACT FROM AUTHOR]

Abstract This paper addresses the problem with respect to finite-time (FT) synchronization for fractional-order (FO) complex networks. Based on hybrid feedback control technique, Lyapunov approach, and some novel analysis techniques of fractional calculation, some sufficient conditions are obtained to guarantee FT synchronization, and the estimation bound of the setting time for synchronization is given. It is meaningful to find that the setting time is dependent on fractional order, controller parameters and initial value of networks. At last, numerical simulations are presented to illustrate the effectiveness and applicability of our proposed control method and verify our theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating discrete-time fractional-order delayed quaternion-valued neural networks (DFDQNNs) by utilizing direct quaternion approach. Firstly, a novel lemma and its two corresponding corollaries have been proposed for estimating nabla fractional difference of the quaternion-valued Lyapunov function. Then, the existence and uniqueness of equilibrium point for DFDQNNs is proved by constructing a new quaternion-valued contraction mapping. In addition, by means of our designed Lyapunov functions and the effective feedback controller as well as neoteric nabla difference inequalities, some sufficient criteria have been obtained to ensure the global Mittag–Leffler stability and Mittag–Leffler synchronization of DFDQNNs, respectively. Finally, some numerical examples are provided to verify the yielded results. [ABSTRACT FROM AUTHOR]

In this article, the fixed-time (FXT) synchronization of discontinuous competitive neural networks (CNNs) involving time-varying delays is investigated. Firstly, two kinds of discontinuous FXT control schemes are proposed and two forms of Lyapunov function are constructed based on p -norm and 1-norm to discuss the FXT synchronization of CNNs. By means of nonsmooth analysis and some inequality techniques, some simple criteria are obtained to achieve FXT synchronization and the upper bound of the settling time with less conservativeness is provided. Furthermore, the effect of time scale on FXT synchronization of CNNs is considered. Lastly, some numerical results for an example are provided to demonstrate the derived theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a class of consensus protocol for detail-balanced networks of agents with general Lipschitz-type nonlinear dynamics and external disturbances is investigated. To guarantee asymptotic consensus in such a multi-agent system, several distributed controllers are constructed based only on the relative state information of neighboring agents. By appropriately constructing Lyapunov function and using tools from M-matrix theory, some sufficient conditions for achieving distributed consensus are provided. Finally, two examples and simulations are given to illustrate the effectiveness of the obtained theoretical result. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the globally exponential synchronization for a class of reaction–diffusion neural networks with Dirichlet boundary conditions and mixed delays is investigated based on periodically intermittent control. Some new and useful synchronization criteria in terms of -norm are derived by introducing multi-parameters, using Lyapunov functional theory. Subsequently, a feasible region of the control parameters for each neuron is derived for the realization of exponential synchronization. Besides, according to the theoretical results, the influences of diffusion strengths and diffusion spaces on synchronization are analyzed and a very interesting fact is revealed that the synchronization of neural networks with reaction–diffusions is more easily realized than those of neural networks without reaction–diffusions. Finally, a reaction–diffusion chaotic network is given to demonstrate the effectiveness of the proposed control methods. [Copyright &y& Elsevier]

Abstract: The global exponential synchronization for a class of delayed reaction-diffusion cellular neural networks with Dirichlet boundary conditions is discussed. Some new sufficient conditions which include the diffusion coefficients are obtained by using the Lyapunov functional method, many real parameters and inequality techniques. Particularly, different from previous works, see references [S. Li, H. Yang, X. Lou, Adaptive exponential synchronization of delayed neural networks with reaction-diffusion terms, Chaos, Solitons Fractals 40 (2009) 930–939; X. Lou, B. Cui, Asymptotic synchronization of a class of neural networks with reaction-diffusion terms and time-varying delayes, Comput. Math. Appl. 52 (2006) 897–904; Y. Wang, J. Cao, Synchronization of a class of delayed neural networks with reaction–diffusion terms, Phys. Lett. A 369 (2007) 201–211], in our results the effect of the diffusion terms on the synchronization are considered for the first time. Finally, a numerical example is given to verify our results. [Copyright &y& Elsevier]

This paper explores finite-time (F-T) synchronization for a type of fully complex-valued (C-V) networks with or without delays by proposing intermittent control schemes but without using the ordinary separation technique. Above all, the vector signum function in complex field is proposed as the generalization of real-valued counterpart, which is critical to the control design in complex field and the construction of Lyapunov functions. To realize F-T synchronization, several complex-valued intermittent controllers, only dependent of the information of controlled nodes, are designed on the addressed complex-valued networks, which are different from the design on the divided real-valued subsystems. In the theoretical analysis, some nontrivial Lyapunov functionals and functions are constructed by virtue of the proposed signum functio n and some inequalities are developed in complex domain to establish criteria of F-T synchronization. Finally, some numerical examples are performed to reveal the effectiveness of the derived results and the practicality of the proposed control strategies. [ABSTRACT FROM AUTHOR]

In this paper, the models of intermittently coupled complex-valued networks (ICCVNs) are presented to reveal the mechanism of intermittent coupling, where the nodes are connected merely in discontinuous time durations. Instead of the common weighted average technique, by proposing a direct error method and constructing piecewise Lyapunov functions, several intermittently adaptive designs are developed to update the complex-valued coupling weights. Especially, an adaptive pinning protocol is designed for ICCVNs with heterogeneous coupling weights and the synchronization is ensured by piecewise adjusting the complex-valued weights of edges within a spanning tree. For ICCVNs with homogeneous coupling weights, based on a connected dominating set, an intermittently adaptive algorithm is developed which just depends on the information of the dominating set with their neighbors. At the end, the established theoretical results are verified by providing two numerical examples. [ABSTRACT FROM AUTHOR]