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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 paper concerns a class of coupled competitive neural networks, subject to disturbance and discontinuous activation functions. To realize the fixed-time quasi-bipartite synchronization, an aperiodic intermittent controller is initially designed. Subsequently, by combining the fixed-time stability theory and nonsmooth analysis, several criteria are established to ensure the bipartite synchronization in fixed time. Moreover, synchronization error bounds and settling time estimates are provided. Finally, numerical simulations are presented to verify the main results. [ABSTRACT FROM AUTHOR]

This article addresses the exponential bipartite synchronization (EBS) of multilayer signed networks with time-varying coupling (MSNs) under aperiodic intermittent-based adaptive dynamic event-triggered control (AAIDETC). Firstly, to increase the elasticity, a novel AAIDETC strategy is presented, whose superiority is that the control gains and the triggering parameters can vary with the evolution of the considered networks. Meanwhile, concerning the aperiodic intermittent control, a new definition of average control ratio (ACR) is put forward, which is more rigorous compared with the relevant results. Then, by the method of ACR, graph theory and Lyapunov approach, the simpler synchronization criterion is gained, which avoids the topology structure of MSNs. Moreover, the EBS issues of Chua's circuits and neural networks established on MSNs are studied, which are two practical applications of our theoretical results. Finally, corresponding numerical simulations are presented to verify the availability of the obtained results. • A new MSN model with time-varying coupling is proposed. • A novel AAIDETC is developed. • An improved definition of average control ratio is presented. [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]

In this paper, synchronization issue of discrete-time fractional fuzzy neural networks (DFFNNs) with delays is solved via quantized control, and is applied in image encryption. Firstly, a novel fractional-order h -difference inequality which makes Lyapunov method more flexible and practical is strictly proved based on the properties of convex functions and theory of discrete fractional calculus. Secondly, by using compression mapping theorem and mathematical induction, we obtain two sufficient conditions to ensure the existence and uniqueness of solutions for DFFNNs. Whereafter, we design a suitable quantized controller, which not only saves channel resources but also reduces control costs. By utilizing our inequality and some analytical techniques, several conservative synchronization criteria for DFFNNs are acquired. Finally, two examples are arranged to illustrate the validity and practicability of our results. • An important fractional difference inequality is strictly proved, which contributes to constructing more flexible Lyapunov functions in the study of discrete-time fractional systems. • Two sufficient conditions are derived to guarantee the existence and uniqueness of the solution for DFFNN with delay by utilizing the compression mapping and mathematical induction. • Discrete-time fractional Halanay inequality is employed to explore synchronization of DFFNNs for the first time. • Under the quantized controller, some easily verifiable synchronization criteria related to step h are acquired. • Based on synchronization of DFFNNs, an image encryption algorithm is designed, and an example is given to verify the encryption effect of our designed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider a type of discrete-time fractional-order complex-valued fuzzy neural networks. First, based on symbolic functions and complex-valued theory, two new inequalities are established to study synchronization problems of networks. Secondly, two simple and original control strategies including linear feedback controller and adaptive controller which can better reduce the control cost, are designed to guarantee quasi-projective synchronization and Mittag-Leffler synchronization of the considered networks, then sufficient synchronization criteria with simplified algebraic conditions are established on the basis of our established lemmas and some inequality techniques. Finally, numerical simulations are given to check effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This work aims to achieve cluster synchronization of a complex network by some pinning control strategies. Firstly, the network not only is affected by the reaction–diffusion and the directed coupling phenomena, but also is disturbed by the stochastic noise and Markovian switching. Secondly, switched constant gain pinning, centralized and decentralized adaptive pinning are proposed respectively to realize the cluster synchronization of the considered network. In these adaptive pinning controllers, the control gain and coupling strength can been adjusted automatically while only a part of the nodes are controlled. Thirdly, the target state of cluster synchronization is taken as the average state related to the directed topology of all nodes in the same cluster, and does not need to be given separately as an isolated node. Finally, to verify the theoretical results, some simulations of directed coupled reaction–diffusion neural networks with stochastic noise and Markovian switching are given. [ABSTRACT FROM AUTHOR]

This paper is concentrated on the fixed/preassigned-time (FXT/PAT) synchronization of multilayered networks, in which the self-dynamics of nodes are heterogeneous and the synchronized state can be an arbitrary prescribed smooth orbit. Above all, the original network is augmented by involving the synchronized state as a virtual node, it is allowed to remove the topological connectivity limitations and reduce the conservatism of the synchronization conditions. Subsequently, several continuous control protocols have been developed to achieve FXT synchronization and some effective criteria are established by utilizing the theorem of FXT stability. Additionally, the relationship is revealed between the estimation of the synchronized time and the layer parameter. Moreover, the PAT synchronization is investigated for a preassigned synchronized time by proposing two control schemes with finite control gains. Eventually, the developed control designs and criteria are validated by some numerical simulations. • FXT/PT synchronization is considered for multilayer networks with a specified state. • The conservatism on topology and criteria is reduced by augmenting original network. • The relationship is revealed between the synchronized time and the layer parameter. [ABSTRACT FROM AUTHOR]

This article addresses the fixed-time (F-T) and predefined-time (P-T) cluster lag synchronization of stochastic multi-weighted complex networks (SMWCNs) via strictly intermittent quantized control (SIQC). Firstly, by exploiting mathematical induction and reduction to absurdity, a novel F-T stability lemma is proved and an accurate estimation of settling time (ST) is obtained. Subsequently, by virtue of the proposed F-T stability, some simple conditions that ensure the F-T cluster lag synchronization of SMWCNs are derived by developing a SIQC strategy. Furthermore, the P-T cluster lag synchronization is also explored based on a SIQC design, where the ST can be predefined by an adjustable constant of the controller. Note that the designed controllers here are simpler and more economical than the traditional design whose the linear part is still activated during the rest interval. Finally, two numerical examples are provided to verify the effectiveness 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]

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]

This article studies the $H_{\infty }$ exponential synchronization problem for complex networks with quantized control input. An aperiodic sampled-data-based event-triggered scheme is introduced to reduce the network workload. Based on the discrete-time Lyapunov theorem, a new method is adopted to solve the sampled-data problem. In view of the aforementioned method, several sufficient conditions to ensure the $H_{\infty }$ exponential synchronization are acquired. Numerical simulations show that the proposed control schemes can significantly reduce the amount of transmitted signals while preserving the desired system performance. [ABSTRACT FROM AUTHOR]

This paper mainly deals with the issue of fixed-time synchronization of fuzzy-based impulsive complex networks. By developing fixed-time stability of impulsive systems and proposing a T-S fuzzy control strategy with pure power-law form, some simple criteria are acquired to achieve fixed-time synchronization of fuzzy-based impulsive complex networks and the estimation of the synchronized time is given. Ultimately, the presented control scheme and synchronization criteria are verified by numerical simulation. [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]

This study addresses the fixed/preset-time bipartite synchronization (FTBS/PTBS) of memristor-based discontinuous multi-layer signed networks via quantized dynamic event-triggered control (ETC). Firstly, a memristor-based neural network model incorporating multi-layer coupling structures, signed networks and discontinuous activations is built. Subsequently, by designing two quantized dynamic ETC strategies without the linear feedback term, the FTBS and PTBS of the considered networks are discussed, and it is proved that Zeno behavior can be ruled out. In contrast to the previous static ETC mechanism, the introduced internal dynamic variable can significantly decrease the triggering times and further save communication resources. Lastly, three numerical examples are offered to verify the correctness and practicability of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This article is devoted to the synchronization of delayed inertial neural systems by virtue of intermittent control scheme. In the proposed inertial models, a type of mixed delays is introduced which is composed of discrete delays and infinite distributed delays. Particulary, the finite distributed delays can be easily obtained by selecting specific kernel functions in infinite distribute delays. To realize exponential synchronization, different from the previous continuous designs for the first-order systems obtained by suitable substitutions of reduced-order, an intermittent control scheme is directly developed for the response inertial systems. Furthermore, a direct analysis method is proposed to derive the synchronization conditions by constructing a Lyapunov functional formed by the state variables and their derivatives. Lastly, the designed control scheme and established criteria are verified via providing a numerical example. [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]

In this paper, without dividing complex-variable networks into two subsystems with real values, the finite-time synchronization is considered for complex-valued dynamical networks with fractional order by means of the theory of complex-variable functions. First of all, as a generalization of the real-valued sign function, the sign functions of complex-valued numbers and complex-valued vectors are introduced and some formulas about them are established. Under the sign function framework, two complex-valued control strategies are designed based on two different norms of complex numbers. Some synchronization criteria are derived and the settling times of synchronization are effectively estimated by developing fractional-order finite-time differential inequalities and utilizing the theory of complex-variable functions. The established theoretical results are demonstrated and the effect of the fractional order of the network model on the finite-time synchronization is revealed finally by providing some numerical simulations. [ABSTRACT FROM AUTHOR]

This article mainly focuses on the problem of synchronization in finite and fixed time for fully complex-variable delayed neural networks involving discontinuous activations and time-varying delays without dividing the original complex-variable neural networks into two subsystems in the real domain. To avoid the separation method, a complex-valued sign function is proposed and its properties are established. By means of the introduced sign function, two discontinuous control strategies are developed under the quadratic norm and a new norm based on absolute values of real and imaginary parts. By applying nonsmooth analysis and some novel inequality techniques in the complex field, several synchronization criteria and the estimates of the settling time are derived. In particular, under the new norm framework, a unified control strategy is designed and it is revealed that a parameter value in the controller completely decides the networks are synchronized whether in finite time or in fixed time. Finally, some numerical results for an example are provided to support the established theoretical results. [ABSTRACT FROM AUTHOR]

This article is concerned with the problem of fixed-time (FXT) and preassigned-time (PAT) synchronization for discontinuous dynamic networks by improving FXT stability and developing simple control schemes. First, some more relaxed conditions for FXT stability are established and several more accurate estimates for the settling time (ST) are obtained by means of some special functions. Based on the improved FXT stability, FXT synchronization for discontinuous networks is discussed by designing a simple controller without a linear feedback term. Besides, the PAT synchronization is also explored by developing several nontrivial control protocols with finite control gains, where the synchronized time can be prespecified according to actual needs and is irrelevant with any initial value and any parameter. Finally, the improved FXT stability and the synchronization for complex networks are confirmed by two numerical examples. [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]

This paper is concerned with the synchronization of fractional-order competitive neural networks with reaction–diffusion terms and time delays. A novel method that combines the fractional-order Lyapunov theorem with M-matrix theory is utilized to cope with synchronization for the addressed networks. Based on such approach and developing two different controllers, some sufficient criteria are derived to guarantee global synchronization by employing the properties about Mittag–Leffler and trigonometric functions, comparison principle as well as the method of contradiction. Finally, a numerical example is provided to show the effectiveness of the established result. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, the issue of the exponential synchronization for complex-valued neural networks with both discrete and distributed delays is investigated by applying impulsive control protocol. Based on the Lyapunov–Krasovskii function, average impulsive interval as well as the comparison principle, some simple verifiable sufficient criteria are established to guarantee the exponential synchronization between the master and the slave systems. Meanwhile, through the serious analysis of the networks systems, the exponential convergence rate can be specified. Additionally, a numerical example is finally given to illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

The study investigates bipartite synchronization of inertial coupled delayed neural networks (ICDNNs) with signed digraph by non-reduced order method and pinning control. The second-order CDNNs will not be converted into a first-order differential system by introducing variable substitution. Instead, a novel Lyapunov–Krasovskii functional is proposed which depends on the topology of the ICDNNs. Some sufficient conditions for linear matrix inequalities (LMI) are derived to realize bipartite synchronization, which is based on matrix decomposition theory and Barbalat Lemma in strongly connected signed networks. And then, M-matrix theory is utilized to generalize the results to networks containing directed spanning trees. Finally, two examples are used to verify the validity of the derived theoretical results. [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]

This paper investigates exponential stability of fractional-order impulsive control systems (FICSs) and exponential synchronization of fractional-order Cohen–Grossberg neural networks (FCGNNs). First, under the framework of the generalized Caputo fractional-order derivative, some new results for fractional-order calculus are established by mainly using L’Hospital’s rule and Laplace transform. Besides, FICSs are translated into impulsive differential equations with fractional-order via utilizing the definition of Dirac function, which reveals that the effect of impulsive control on fractional systems is dependent of the order of the addressed systems. Furthermore, exponential stability of FICSs is proposed and some novel criteria are obtained by applying average impulsive interval and the method of induction. As an application of the stability for FICSs, exponential synchronization of FCGNNs is considered and several synchronization conditions are established under impulsive control. Finally, several numerical examples are provided to illustrate the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

In this paper, without transforming the quaternion-valued neural networks into two equivalent complex-valued systems or four equivalent real-valued systems, a novel class of fractional-order quaternion-valued neural networks with leakage and discrete delays is investigated. To this end, two novel inequalities are established with the aid of properties of quaternion and Caputo fractional derivative. By exploiting Lyapunov method, our established inequalities, fractional-order Razumikhin theorem and some analysis techniques, some criteria ensuring the global asymptotical synchronization and the global Mittag-Leffler synchronization of the considered networks are obtained through designing suitable controllers. Finally, two numerical examples are utilized to show the derived theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, spatial diffusions are introduced to fractional-order coupled networks and the problem of synchronization is investigated for fractional-order coupled neural networks with reaction-diffusion terms. First, a new fractional-order inequality is established based on the Caputo partial fractional derivative. To realize asymptotical synchronization, two types of adaptive coupling weights are considered, namely: 1) coupling weights only related to time and 2) coupling weights dependent on both time and space. For each type of coupling weights, based on local information of the node’s dynamics, an edge-based fractional-order adaptive law and an edge-based fractional-order pinning adaptive scheme are proposed. Furthermore, some new analytical tools, including the method of contradiction, L’Hopital rule, and Barbalat lemma are developed to establish adaptive synchronization criteria of the addressed networks. Finally, an example with numerical simulations is provided to illustrate the validity and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Projective synchronization (PS) is a type of chaos synchronization where the states of slave system are scaled replicas of the states of master system. This paper studies the asymptotic projective synchronization (APS) between master–slave chaotic neural networks (NNs) with mixed time-delays and unmatched coefficients. Based on useful inequality techniques and constructing a suitable Lyapunov functional, some simple criteria are derived to ensure the APS of considered networks via designing a novel adaptive feedback controller. In addition, a numerical example and its MATLAB simulations are provided to check the feasibility of the obtained results. The main innovation of our work is that we dealt with the APS problem between two different chaotic NNs, while most of the existing works only concerned with the PS of chaotic systems with the same topologies. In addition, compared with the controllers introduced in the existing papers, the designed controller in this paper does not require any knowledge about the activation functions, which can be seen as another novelty of the paper. [ABSTRACT FROM AUTHOR]

This work investigates the H ∞ output synchronization (HOS) of the directed coupled reaction–diffusion (R–D) neural networks (NNs) with mixed delays. Firstly, a model of the directed state coupled R–D NNs is introduced, which not only contains some discrete and distributed time delays, but also obeys a mixed Dirichlet–Neumann boundary condition. Secondly, a spacial sampled-data controller is proposed to achieve the HOS of the considered networks. This type of controller can reduce the update rate in the process of control by measuring the state of networks at some fixed sampling points in the space region. Moreover, some criteria for the HOS are established by designing an appropriate Lyapunov functional, and some quantitative relations between diffusion coefficients, mixed delays, coupling strength and control parameters are given accurately by these criteria. Thirdly, the case of directed spatial diffusion coupled networks is also studied and, the following finding is obtained: the spatial diffusion coupling can suppress the HOS while the state coupling can promote it. Finally, one example is simulated as the verification of the theoretical results. • H ∞ output synchronization for the directed coupled R–D NNs is defined. • A spacial sampled-data controller is proposed to lower spatial update rate. • Obtained conditions depend on diffusion, delay, and control parameters. • Both the directed state and spatial diffusion coupled R–D NNs are considered. • Synchronization can be suppressed by diffusion and promoted by state couple. [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]

Compared to other types of synchronization such as complete synchronization and lag synchronization, there is a unique advantage in projective synchronization since it can greatly improve the security of communication. In this paper, the projective synchronization problem of a class of chaotic neural networks with time-varying delay is investigated via designing a novel adaptive controller. Some simple and useful criteria are derived by employing Lyapunov functional method and Lagrange mean value theorem. Finally, an example and its numerical simulations are given to demonstrate the effectiveness of the proposed control schemes. It is worth to mention that the designed controller in this paper dos not require any knowledge about the activation functions, which can be seen the main novelty of the paper. [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]

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]

This article concerns the fixed-time (FET) and prescribed-time (PET) synchronization of quaternion-valued fuzzy BAM neural networks via aperiodic intermittent pinning control. First of all, two improved inequalities for FET and PET stability are proposed to reduce the conservatism of existing results in theoretical analysis. Subsequently, by excluding the control input of the rest interval in previous semi-intermittent design, two novel quaternion-valued aperiodic intermittent pinning controllers are developed. Furthermore, regarding the original quaternion-valued networks as an entirety instead of decomposing it into four real-valued subnetworks, several sufficient criteria that ensure the FET and PET synchronization of quaternion-valued fuzzy BAM neural networks are obtained by means of the improved stability inequalities and the designed controllers. Finally, the validity of the theoretical results is verified by three numerical examples. [ABSTRACT FROM AUTHOR]