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In this paper, the fixed-time and preassigned-time synchronization issues of fully quaternion-valued fuzzy memristive neural networks are studied based on the dynamic event-triggered control mechanism. Initially, the fuzzy rules are defined within the quaternion domain and the relevant properties are established through rigorous analysis. Subsequently, to conserve resources and enhance the efficiency of the controller, a kind of dynamic event-triggered control mechanism is introduced for the fuzzy memristive neural networks. Based on the non-separation analysis, fixed-time and preassigned-time synchronization criteria are presented and the Zeno phenomenon under the event-triggered mechanism is excluded successfully. Finally, the effectiveness of the theoretical results is verified through numerical simulations. [ABSTRACT FROM AUTHOR]

This article is concerned with fixed-time synchronization and preassigned-time synchronization of Cohen–Grossberg quaternion-valued neural networks with discontinuous activation functions and generalized time-varying delays. Firstly, a dynamic model of Cohen–Grossberg neural networks is introduced in the quaternion field, where the time delay successfully integrates discrete-time delay and proportional delay. Secondly, two types of discontinuous controllers employing the quaternion-valued signum function are designed. Without utilizing the conventional separation technique, by developing a direct analytical approach and using the theory of non-smooth analysis, several adequate criteria are derived to achieve fixed-time synchronization of Cohen–Grossberg neural networks and some more precise convergence times are estimated. To cater to practical requirements, preassigned-time synchronization is also addressed, which shows that the drive-slave networks reach synchronization within a specified time. Finally, two numerical simulations are presented to validate the effectiveness of the designed controllers and criteria. [ABSTRACT FROM AUTHOR]

This study sets out to solve the synchronization problem of complex-valued multi-layer coupled systems (CVMLCSs) under two asynchronous intermittent event-triggered mechanisms (IETMs). Unlike the existing works on IETM, two kinds of novel IETMs including static IETM and dynamic IETM are developed, where the asynchronous nature is mainly reflected in the fact that each node in each layer possesses its own control and rest intervals. Remarkably, under two control schemes, the choice of control time sequence is based on corresponding event-triggered condition rather than being preset artificially. Moreover, by utilizing graph theory and Lyapunov approach, two synchronization conditions for CVMLCSs are given, respectively. In the end, as an application, a complex-valued multi-layer neural network model is established and some numerical examples are provided to validate the feasibility of the theoretical results. • A new model of time-varying complex-valued multi-layer coupled systems is built. • Two novel asynchronous intermittent event-triggered mechanisms are proposed. • Two controllers remove the limitation on artificial selection of control time sequence. [ABSTRACT FROM AUTHOR]

In this paper, a complex-variable neural network model is obtained for solving complex-variable optimization problems described by differential inclusion. Based on the nonpenalty idea, the constructed algorithm does not need to design penalty parameters, that is, it is easier to be designed in practical applications. And some theorems for the convergence of the proposed model are given under suitable conditions. Finally, two numerical examples are shown to illustrate the correctness and effectiveness of the proposed optimization model. [ABSTRACT FROM AUTHOR]

A neural network model upon differential inclusion is designed for solving the complex-variables convex programming, and the chain rule for real-valued function with the complex-variables is established in this paper. The model does not need to choose penalty parameters when applied to practical problems, which makes it easier to design. The result is obtained that its state reaches the feasible region in finite time. Furthermore, the convergence for its state to an optimal solution is proved. Some typical examples are shown for the effectiveness of the designed model. [ABSTRACT FROM AUTHOR]

In this paper, we have made an effort to investigate the general decay projective synchronization (GDPS) problem of a type of delayed memristor-based BAM neural networks. First, we introduced a type of novel nonlinear controller. Then, we derived some sufficient conditions ensuring the GDPS of considered networks by employing differential inclusion theory and using well-known Lyapunov functional method. Lastly, an example is given to show the correctness of obtained results. To the authors' knowledge, the results derived in this paper are the only available ones on the projective synchronization of BAM neural networks, combining the three main factors, i.e., memristor, general decay and time-varying delays. [ABSTRACT FROM AUTHOR]

This paper concerns the topic of exponential synchronization for a class of memristive Cohen-Grossberg neural networks with time-varying delays by designing a suitable controller. Through a nonlinear transformation, we obtain an alternative system from the considered memristive Cohen-Grossberg neural networks. Then, by studying the exponential synchronization of the alternative system, we get some novel and effective exponential synchronization criteria for the considered memristive Cohen-Grossberg neural networks. These results generalize some previous known results and remove a few restrictions on control width and time-delays. Finally, numerical simulations are given to present the effectiveness of the 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]

In this paper, the cluster consensus problem with delays of first-order nonlinear multi-agent systems is studied through pinning leader-following approach with periodic intermittent effect. The graph of the networked system is assumed to be directed and weakly connected. A new type of pinning consensus protocol with intermittent effect is designed according to the ways in which the agents link, specifically, the agents in each cluster are divided into three subsets due to the orientation of their topological degree, and each subset of agents is controlled by an individual law. A redefined notion on cluster consensus with two sorts of time delays is proposed in this article. Some consensus criteria are derived to guarantee that the agents in the same cluster asymptotically follow the virtual leader with a delay, while agents in different clusters reach consensus with delays via following their leaders. Some numerical simulations are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The exponential synchronization of hybrid coupled reaction–diffusion neural networks with time delays is discussed in this article. At first, a generalized intermittent control with spacial sampled-data is introduced, which is intermittent in time and data sampling in space. This type of control strategy not only can unify the traditional periodic intermittent control and the aperiodic case, but also can lower the update rate of the controller in both temporal and spatial domains. Next, based on the designed control protocol and the Lyapunov–Krasovskii functional approach, some novel and readily verified criteria are established to guarantee the exponential synchronization of the considered networks. These criteria depend on the diffusion coefficients, coupled strengths, time delays as well as control parameters. Finally, the effectiveness of the proposed control strategy is shown by a numerical example. [ABSTRACT FROM AUTHOR]

This paper considers the delay-dependent stability of memristive complex-valued neural networks (MCVNNs). A novel linear mapping function is presented to transform the complex-valued system into the real-valued system. Under such mapping function, both continuous-time and discrete-time MCVNNs are analyzed in this paper. Firstly, when activation functions are continuous but not Lipschitz continuous, an extended matrix inequality is proved to ensure the stability of continuous-time MCVNNs. Furthermore, if activation functions are discontinuous, a discontinuous adaptive controller is designed to acquire its stability by applying Lyapunov–Krasovskii functionals. Secondly, compared with techniques in continuous-time MCVNNs, the Halanay-type inequality and comparison principle are firstly used to exploit the dynamical behaviors of discrete-time MCVNNs. Finally, the effectiveness of theoretical results is illustrated through numerical examples. [ABSTRACT FROM AUTHOR]

The global stability problem for a class of complex-valued neural networks with both mixed time delays and impulsive effect is concerned in this literature. By using Schur complement, forming an equivalent matrix, and constructing an appropriate Lyapunov functional, some new sufficient criteria to ascertain the existence, uniqueness, globally exponential stability and globally asymptotical stability of the equilibrium point of complex-valued neural networks are obtained in terms of linear matrix inequality techniques. Meanwhile, several linear matrix inequalities have been proved in the literature, which shall be used to prove the stability of the equilibrium point. Finally, simulation results of one numerical example are also delineated to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the exponential synchronization, finite time synchronization, and fixed-time synchronization of Cohen–Grossberg neural networks (CGNNs) with discontinuous activations and time-varying delays. Discontinuous feedback controller and Novel adaptive feedback controller are designed to realize global exponential synchronization, finite time synchronization and fixed-time synchronization by adjusting the values of the parameters ω in the controller. Furthermore, the settling time of the fixed-time synchronization derived in this paper is less conservative and more accurate. Finally, some numerical examples are provided to show the effectiveness and flexibility of the results derived in this paper. [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]

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, the exponential lag synchronization for a class of Cohen–Grossberg neural networks with discrete time-delays and distributed delays is investigated via periodically intermittent control. Some simple and useful criteria are derived by using mathematical induction method and the analysis technique which are different from the methods employed in correspondingly previous works. Finally, two examples and their numerical simulations are given to demonstrate the effectiveness of the proposed control schemes. [ABSTRACT FROM AUTHOR]

This paper investigates the exponential synchronization of delayed memristor-based neural networks (MNNs) with discontinuous activation functions. Based on the framework of Filippov solution and differential inclusion theory, using new analytical techniques and introducing suitable Lyapunov functionals, some novel sufficient conditions ensuring the exponential synchronization of considered networks are established via two types of discontinuous controls: linear feedback control and adaptive control. In particular, we extend the discontinuous control strategies for neural networks with continuous dynamics to MNNs with discontinuous activations. Numerical simulations are given to show the effectiveness of the theoretical results. Our approach and theoretical results have a leading significance in the design of synchronized MNN circuits involving discontinuous activations and time-varying delays. [ABSTRACT FROM AUTHOR]

This paper investigates a new type of stability, namely global generalized exponential stability of the nonautonomous delayed cellular neural networks. Several novel delay-dependent sufficient conditions are established by applying a new generalized Halanay inequality. In these conditions, the boundedness of time-varying delays and coefficients are not required. In addition, the effectiveness of these conditions is illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]

This paper concerns the problem of global and local finite-time synchronization for a class of memristor-based Cohen–Grossberg neural networks with time-varying delays by designing an appropriate feedback controller. Through a nonlinear transformation, we derive an alternative system from the considered memristor-based Cohen–Grossberg neural networks. Then, by considering the finite-time synchronization of the alternative system, we obtain some novel and effective finite-time synchronization criteria for the considered memristor-based Cohen–Grossberg neural networks. These results generalize and extend some previous known works on conventional Cohen–Grossberg neural networks. Finally, numerical simulations are given to present the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks are guaranteed by Chain rule and inequalities technique. Moreover, a new method involving Yoshizawa-like theorem is favorably employed to acquire the existence of periodic solution. By applying the theory of set-valued maps and functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks. The obtained results expand and complement some previous work on memristor-based BAM neural networks. Finally, a numerical example is provided to show the applicability and effectiveness of our theoretical results. [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]

Memristive network exhibits state-dependent switching behaviors due to the physical properties of memristor, which is an ideal tool to mimic the functionalities of the human brain. In this paper, finite-time synchronization is considered for a class of memristor-based neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, several new sufficient conditions ensuring the finite-time synchronization of memristor-based chaotic neural networks are obtained by using analysis technique, finite time stability theorem and adding a suitable feedback controller. Besides, the upper bounds of the settling time of synchronization are estimated. Finally, a numerical example is given to show the effectiveness and feasibility of the obtained results. [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]

In this paper, the exponential synchronization for a class of complex networks with finite distributed delays coupling is studied via periodically intermittent control. Some novel and useful criteria are derived by utilizing a different technique compared with some correspondingly previous results. As a special case, some sufficient conditions ensuring the exponential synchronization for a class of coupled neural networks with distributed delays are obtained. Furthermore, a feasible region of the control parameters is derived for the realization of exponential synchronization. It is worth noting that the synchronized state in this paper is not an isolated node but a non-decoupled state, in which the inner coupling matrix and the degree of the nodes play a central role. Additionally, the traditional assumptions on control width, non-control width, and discrete delays are removed in our results. Finally, some numerical simulations are given to demonstrate the effectiveness of the proposed control method. [ABSTRACT FROM PUBLISHER]

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: 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 mainly study the distribution of the roots of a fifth degree exponential polynomial. We obtain the sufficient and necessary conditions for the existence of purely imaginary roots of the exponential polynomial. Applying the obtained results, we consider a neural network model consisting of five neurons with delays. The sum of delays is regarded as the bifurcation parameter. Under some conditions, we show that the zero solution is locally asymptotically stable when the time delay is suitably small, while change of stability of zero solution will cause a bifurcating periodic solution as the time delay passes through a certain critical value. In order to illustrate our theoretical analysis, some numerical simulations are presented. [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 paper, we investigate bidirectional associative memory Cohen–Grossberg neural networks with time delays. By applying the Young inequality technique, Dini derivative, and introducing many real parameters, a series of new and useful criteria on the existence and uniqueness of an equilibrium point and its global asymptotical stability are established. It is shown that in some special cases of the results, the stability criteria can be easily checked. Finally, an example is given to illustrate the result obtained in this paper. [Copyright &y& Elsevier]

Abstract: In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with recent history distributed delays and impulses are considered. By using Lyapunov functional method and fixed point theorem, we derive several sufficient conditions for the existence and globally exponential stability of a unique periodic solution of the networks. The results of this paper are new and different from previously known results. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the periodic neural networks with variable coefficients and time-varying delays, and investigate the existence of periodic solution and its global exponential stability. Various sufficient conditions ensuring the existence of periodic and its global exponential stability are given. The results obtained in this paper extend and generalize those given in previous literature. [Copyright &y& Elsevier]

Abstract: This Letter studies the Cohen–Grossberg networks dynamical systems with variable coefficients and time-varying delays. By applying the Young inequality technique, Dini derivative and introducing many real parameters, and estimating the upper bound of solutions of the system, a series of new and useful criteria on the boundedness, global exponential stability are established. The results obtained in this Letter extend and generalize the corresponding results existing in previous literature. [Copyright &y& Elsevier]

Abstract: This paper studies the general neural networks dynamical systems with variable coefficients and time-varying delays. By applying the Young inequality technique, Dini derivative and introducing many real parameters, and estimating the upper bound of solutions of the system, a series of new and useful criteria on the boundedness, global exponential stability and the existence and global exponential stability of the periodic solutions are established. Particularly, when the system degenerates into the autonomous case, the new criteria on the existence, uniqueness and global exponential stability of the equilibrium points are obtained. The results obtained in this paper extend and generalize the corresponding results existing in previous literature. [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]

In this paper, a class of nonautonomous cellular neural networks is studied. By constructing a suitable Liapunov functional, applying the boundedness theorem for general functional–differential equations and the Banach fixed point theorem, a series of new criteria are obtained on the boundedness, global exponential stability, and existence of periodic solutions. [Copyright &y& Elsevier]

This paper studies the general decay synchronization of a class of bidirectional associative memory neural networks with time-varying delays. First, a useful lemma which generalizes the classical exponential synchronization and polynomial synchronization is introduced. Then by using this lemma, some simple sufficient criteria ensuring the general decay synchronization of considered bidirectional associative memory neural networks are obtained via designing a novel nonlinear feedback controller and using some inequality techniques. Finally, two numerical examples are provided to demonstrate the feasibility of the established theoretical results. The results of this paper are general since the classical polynomial synchronization and exponential synchronization can be seen the special cases of general decay synchronization. [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]

Abstract: In this paper, the global projective synchronization of fractional-order neural networks is investigated. First, a sufficient condition in the sense of Caputo’s fractional derivation to ensure the monotonicity of the continuous and differential functions and a new fractional-order differential inequality are derived, which play central roles in the investigation of the fractional adaptive control. Based on the preparation and some analysis techniques, some novel criteria are obtained to realize projective synchronization of fractional-order neural networks via combining open loop control and adaptive control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization of the addressed neural networks. Finally, an example with numerical simulations is given to show the effectiveness of the obtained results. [Copyright &y& Elsevier]