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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]

The asymptotic synchronization of quaternion-valued delayed neural networks with impulses and inertia is studied in this article. Firstly, a convergence result on piecewise differentiable functions is developed, which is a generalization of the Barbalat lemma and provides a powerful tool for the convergence analysis of discontinuous systems. To achieve synchronization, a constant gain-based control scheme and an adaptive gain-based control strategy are directly proposed for response quaternion-valued models. In the convergence analysis, a direct analysis method is developed to discuss the synchronization without using the separation technique or reduced-order transformation. In particular, some Lyapunov functionals, composed of the state variables and their derivatives, are directly constructed and some synchronization criteria represented by matrix inequalities are obtained based on quaternion theory. Some numerical results are shown to further confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

Currently, through proposing discontinuous control strategies with the signum function and discussing separately short-term memory (STM) and long-term memory (LTM) of competitive artificial neural networks (ANNs), the fixed-time (FXT) synchronization of competitive ANNs has been explored. Note that the method of separate analysis usually leads to complicated theoretical derivation and synchronization conditions, and the signum function inevitably causes the chattering to reduce the performance of the control schemes. To try to solve these challenging problems, the FXT synchronization issue is concerned in this paper for competitive ANNs by establishing a theorem of FXT stability with switching type and developing continuous control schemes based on a kind of saturation functions. Firstly, different from the traditional method of studying separately STM and LTM of competitive ANNs, the models of STM and LTM are compressed into a high-dimensional system so as to reduce the complexity of theoretical analysis. Additionally, as an important theoretical preliminary, a FXT stability theorem with switching differential conditions is established and some high-precision estimates for the convergence time are explicitly presented by means of several special functions. To achieve FXT synchronization of the addressed competitive ANNs, a type of continuous pure power-law control scheme is developed via introducing the saturation function instead of the signum function, and some synchronization criteria are further derived by the established FXT stability theorem. These theoretical results are further illustrated lastly via a numerical example and are applied to image encryption. [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]

This paper is mainly devoted to fixed/preassigned-time synchronization problem for a type of full complex-variable BAM neural networks (BAMNNs) by means of direct analysis method to replace the classical decomposition approach. Above all, under the framework of the complex-valued signum function and two different forms of norms, several effective complex-valued control strategies are directly developed to ensure fixed-time synchronization, and the derived criteria are less conservative than the previous related results. In addition, the preassigned-time synchronization is also considered by directly designing some complex-valued control laws with bounded control gains, in which the synchronization time can be preset arbitrarily in advance within the actual allowable range. The theoretical results are lastly supported via numerical examples. [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 paper concerns with the event-based dynamic output feedback control for the synchronization of fuzzy neural networks under mixed delay and deception attacks. A weighted sum-based dynamic event-triggered mechanism (WSDETM) is developed to save the communication resources while preserving a satisfactory system performance. A dynamic output feedback controller (DOFC) is designed to achieve exponential synchronization of fuzzy neural networks. To reduce the data traffic, both communication channels from the sensor to DOFC and DOFC to Zero-Order Holder are subject to WSDETM. Different from the traditional deception attacks modeled by Bernoulli process, we adopt the more general Markov process modeling deception attacks. By using the cone-complimentarity linearization algorithm, the DOFC and WSDETM parameters are carried out. The effectiveness of the proposed method is demonstrated with two numerical cases. [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 paper deals with the problems of quasi‐projective synchronization (QPS) and finite‐time synchronization (FTS) for a kind of delayed fractional‐order BAM neural networks (DFOBAMNNs). In order to reach the goals of synchronization and more accurately gauge of settling time and error level, several fresh quantized controllers are structured to make the utmost of confined communication resources. Then, based on the finite‐time theorem, quantized control strategy, Lyapunov function theory and properties of Mittag–Leffler function as well as inequality analysis techniques, some plentiful criteria are formed to set up a relation between control gains and quantization parameters. In addition, the corresponding error bound of QPS and guages of the settling time on FTS are also given. Finally, a few numerical examples are introduced to validate the effectiveness of the presented control protocols. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating the synchronization of fractional-order output-coupling multiplex networks (FOOCMNs). Firstly, a type of fractional-order multiplex network is introduced, where the intra-layer coupling and the inter-layer coupling are described separately, and nodes communicate with each other by their outputs, which is more realistic when the node states are unmeasured. By using the Lyapunov method and the fractional differential inequality, sufficient conditions are provided for achieving asymptotic synchronization based on the designed adaptive control, where the synchronized state of each layer is different. Furthermore, a quantized adaptive controller is developed to realize the synchronization of FOOCMNs, which effectively reduces signal transmission frequency and improves the effective utilization rate of network resources. Two numerical examples are given at last to support the theoretical analysis. [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 is dedicated to the asymptotic stability and synchronization for a type of fractional complex-valued inertial neural network by developing a direct analysis method. First, a new fractional differential inequality is presented for nonnegative functions, which provides an effective tool for the convergence analysis of fractional-order systems. Moreover, instead of the previous separation analysis for complex-valued neural networks, a class of Lyapunov functions composed of the complex-valued states and their fractional derivatives is constructed, and some compact stability criteria are derived. In synchronization analysis, unlike the existing control schemes for reduced-order subsystems, some feedback and adaptive control schemes, formed by the linear part and the fractional derivative part, are directly designed for the response fractional inertial neural networks, and some synchronization conditions are derived using the established fractional inequality. Finally, the theoretical analysis is supported via two numerical examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the issue of fixed-time (FT) and preassigned-time (PT) synchronization of impulsive complex networks (ICNs) with mismatched parameters. Firstly, several more succinct conditions are established to achieve FT stability of impulsive systems and an improved estimation for the stable time is given. Subsequently, based on the improved FT stability results, the FT synchronization criteria for ICNs with mismatched parameters are proposed by designing fixed-time controllers without the linear part. Correspondingly, the PT synchronization problem is also considered by developing several innovative control protocols, where the synchronized time can be arbitrary predefined according to task demands and the control gains are bounded. Ultimately, the presented synchronization criteria are verified by numerical simulation. [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]

The issues of complete synchronization (CS) and finite-time synchronization (F-TS) for a class of fractional-order fuzzy neural networks are addressed based on nonlinear feedback control in this paper. First, a fractional-order finite-time convergence principle is established by virtue of fractional calculus basic theory and reduction to absurdity. Next, two novel nonlinear controllers, namely the adaptive nonlinear controller and discontinuous nonlinear controller, are designed. Then some easily validated criteria to guarantee CS and F-TS are derived with the help of some useful analysis techniques and our newly established convergence principle. Moreover, the settling time of F-TS is effectively estimated. Finally, some numerical results are presented to show the validity of derived theoretical 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 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 paper, the exponential synchronization of directed spatio-temporal complex networks is concerned via intermittent pinning control, where the underlying topology is very generic and is not necessarily node balanced or strongly connected. Firstly, based on the decomposition of the topological graph into several maximal strongly connected subgraphs, two intermittent pinning controllers are developed. Subsequently, by adding the synchronized state as a virtual node to the original network, the exponential pinning synchronization of the underlying network is discussed, and several sufficient criteria are derived by utilizing M -matrix and LMI technique. Finally, the feasibility of theoretical results is substantiated by an illustrative example. [ABSTRACT FROM AUTHOR]

This article is dedicated to the synchronization problem of fractional-order spatiotemporal networks with boundary coupling. Above all, instead of the traditional coupling form at the whole space, a type of boundary communication mechanism is proposed for fractional-order spatiotemporal networks, where nodes interact each other only at the spatial boundary. Subsequently, based on fractional-order inequalities and various analytical skills, some synchronization criteria are derived for the addressed networks with boundary constant weights or time-varying weights. Particularly, an adaptive scheme and its pinning form are designed to update time-varying coupling weights only based on the states information at the boundary position, which are more effective and convenient compared to the existing adaptive strategies dependent of states information in whole space. In addition, a rigorous theoretical analysis is developed for fractional-order adaptive strategy, which provides a new analytic method for adaptive control of fractional-order models. Lastly, the theoretical analysis is confirmed by 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]

In this paper, the problem of synchronization for a class of fractional-order delayed spatio-temporal neural networks with Dirichlet boundary conditions is investigated. Firstly, based on the L'Hopital law, a Caputo fractional partial differential inequality with p -norm is established to improve the previous results. Besides, a generalized fractional-order Halanay inequality is introduced by rigorous theoretical deduction. Additionally, to realize synchronization, two different control schemes are designed for the networks, respectively, and several criteria are derived based on the developed fractional inequalities. Finally, numerical examples and simulations are provided to verify the correctness of the 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]

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 article, the fixed-time (FIT) and preassigned-time (PRT) stability of nonlinear models and the FIT/PRT synchronization of discontinuous delayed fuzzy Cohen–Grossberg neural networks (DFCGNNs) are explored, respectively. Firstly, by means of hyperbolic-cosine function and Gudermannian function, a novel FIT stability theorem is established by utilizing Lyapunov method. Then, based on the developed stability theorem, several new discontinuous control schemes with hyperbolic-cosine function are developed to discuss the FIT synchronization of DFCGNNs. Furthermore, the PRT synchronization is also explored by slightly modifying FIT control schemes, where the synchronization time is predetermined. Eventually, two numerical examples are provided to validate the theoretical research. [ABSTRACT FROM AUTHOR]

This paper is primarily concentrated on finite-time cluster synchronization of fractional-order complex-variable networks with nonlinear coupling by utilizing the non-decomposition method. Firstly, two control strategies are designed which are relevant to complex-valued sign functions. Thereafter, by employing fractional-order stability theory and complex function theory, several criteria are deduced to ensure finite-time cluster synchronization under the framework within a new norm consisting of absolute values for real and imaginary components. Furthermore, the setting time is effectively estimated based on some significant properties of fractional-order Caputo derivation and Mittag-Leffler functions. Lastly, two numerical examples are given to verify the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

This article investigates the global stabilization problem of Takagi–Sugeno fuzzy memristor-based neural networks with reaction–diffusion terms and distributed time-varying delays. By using the Green formula and proposing fuzzy feedback controllers, several algebraic criteria dependent on the diffusion coefficients are established to guarantee the global exponential stability of the addressed networks. Moreover, a simpler stability criterion is obtained by designing an adaptive fuzzy controller. The results derived in this article are generalized and include some existing ones as special cases. Finally, the validity of the theoretical results is verified by two examples. [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]

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]

This paper mainly deals with the problem of exponential and adaptive synchronization for a type of inertial complex-valued neural networks via directly constructing Lyapunov functionals without utilizing standard reduced-order transformation for inertial neural systems and common separation approach for complex-valued systems. At first, a complex-valued feedback control scheme is designed and a nontrivial Lyapunov functional, composed of the complex-valued state variables and their derivatives, is proposed to analyze exponential synchronization. Some criteria involving multi-parameters are derived and a feasible method is provided to determine these parameters so as to clearly show how to choose control gains in practice. In addition, an adaptive control strategy in complex domain is developed to adjust control gains and asymptotic synchronization is ensured by applying the method of undeterminated coefficients in the construction of Lyapunov functional and utilizing Barbalat Lemma. Lastly, a numerical example along with simulation results is provided to support the theoretical work. [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]

In this paper, without separating complex-valued neural networks into two real-valued systems, the finite-time synchronization is addressed for a class of fully complex-valued neural networks with fractional-order. Firstly, a new fractional-order differential inequality is established to improve some existing results in the real domain. Besides, to avoid the traditional separation method, the sign function of complex numbers is proposed and some properties about it are derived. Under the proposed sign function framework, by designing some novel and effective control schemes, constructing nontrivial Lyapunov functions and developing some new inequality methods in complex domain, several criteria of finite-time synchronization are derived and the settling-time of synchronization is effectively estimated. Finally, the effectiveness of the theoretical results is demonstrated by some numerical examples. [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]

This paper studies quasi-projective synchronization (QPS) and complete synchronization (CS) for a class of fractional-order complex-valued neural networks with time delays by designing suitable controllers. To realize QPS and CS, linear feedback controller and adaptive controller are designed, and a novel fractional-order differential inequality is built by means of Laplace transform and properties of Mittag-Leffler function. By utilizing Lyapunov method, our proposed inequality, fractional-order Razumikhin theorem and some complex analysis techniques, some effective criteria are derived to ensure QPS and CS of the considered networks. Furthermore, the error bound of QPS is obtained. Finally, some numerical results are given to demonstrate the effectiveness of the presented theoretical results. [ABSTRACT FROM AUTHOR]