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This paper tries to study the problem of finite-time synchronization for delayed semi-Markov reaction–diffusion systems. Based on the spatial and parametric characteristics of the considered systems, a new asynchronous boundary control scheme is proposed to ensure the finite-time synchronization of the drive and response systems. In the asynchronous boundary control scheme, only an actuator should be placed at the spatial boundary, which is more easier to implement and economical than the other non-boundary control strategies. Besides, the system parameters and controller follow two asynchronous semi-Markov chains for jumping, which is more practical than obeying one semi-Markov chain. Moreover, for the considered systems, we proposes a new lemma of finite-time stability, and by employing the inequality methods and variable substitution, we derive the criterion of finite-time synchronization and a correlative corollary. Finally, a numerical example and an application example on secure communication are carried out to support the developed approach. • Our study enriches the related research of semi-Markov RDSs. The obtained results guarantee the finite-time synchronization of semi-Markov RDSs, which is more effective and practical than asymptotic synchronization. • This paper proposes a novel asynchronous boundary control scheme, for the synchronization of semi-Markov RDSs. Compared with existing ones, our control scheme has obvious advantages in realizability and economy. • Based on the existing papers, in the designed controller, a constant is introduced, such that the intense chatter of controller could be reduced. • For the considered systems and designed controller, a new finite-time stability lemma is proposed, which enables the derivation of a finite-time synchronization criterion and a related corollary of this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization problem of switched systems with mismatched modes by an event-triggered control approach. A hybrid event-triggered scheme (HETS) with a dynamically adjustable threshold is newly proposed, which combines periodic sampling, continuous event-trigger and slow switching. It is assumed that the modes and states of the controller are updated only at each triggering instant, so the situation of asynchronous switching could arise. Compared with the control strategy under static HETS, the proposed hybrid event-triggered control strategy has the advantage of potentially speeding up the stabilization while reducing the communication burden. To ease the analysis, the closed-loop system is accordingly represented as a combination of the switched system with a periodically sampled control input and the one with a continuously event-triggered control input. By considering input delay information in the construction of multiple Lyapunov–Krasovskii functional (LKF), a discontinuous and non-positive definite LKF is developed to establish sufficient conditions on the exponential stability for the closed-loop switched system. The design method of the desired controller and HETS is then provided. Finally, the result obtained in this paper is applied to a networked continuous stirred tank reactors system. • A hybrid event-triggered control scheme is newly proposed for the switched systems. • Based on the scheme, a special closed-loop system is presented to ease the analysis. • Multiple Lyapunov–Krasovskii functional with less constraint is developed. • The result is finally applied to a networked continuous stirred tank reactors system. [ABSTRACT FROM AUTHOR]

Robust stability of different types of dynamical neural network models including time delay parameters have been extensively studied, and many different sets of sufficient conditions ensuring robust stability of these types of dynamical neural network models have been presented in past decades. In conducting stability analysis of dynamical neural systems, some basic properties of the employed activation functions and the forms of delay terms included in the mathematical representations of dynamical neural networks are of crucial importance in obtaining global stability criteria for dynamical neural systems. Therefore, this research article will examine a class of neural networks expressed by a mathematical model that involves the discrete time delay terms, the Lipschitz activation functions and possesses the intervalized parameter uncertainties. This paper will first present a new and alternative upper bound value of the second norm of the class of interval matrices, which will have an important impact on obtaining the desired results for establishing robust stability of these neural network models. Then, by exploiting wellknown Homeomorphism mapping theory and basic Lyapunov stability theory, we will state a new general framework for determining some novel robust stability conditions for dynamical neural networks possessing discrete time delay terms. This paper will also make a comprehensive review of some previously published robust stability results and show that the existing robust stability results can be easily derived from the results given in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we consider a two dimensional PDE model describing the proliferation-invasion structure of hypoxic glial cells in the brain, in which the cell movement is determined not only by natural diffusion but also, by the gradient of the concentration of oxygen. This model is given by a second order nonlinear system involving the density of cancer cells and the oxygen concentration, which are coupled by a chemoattraction term, a source of logistic growth, and a reaction term of Michaelis-Menten type. The contribution of this paper is summarized in the following two main aspects: first, we prove the existence and uniqueness of strong solutions; and second, we propose a nonlinear fully discrete finite element (FE) approximation for the model. We prove its well-posedness, some uniform estimates, the positivity for the discrete oxygen concentration and approximated positivity for the discrete tumour cells, which are required in this biological model. The key point to develop the numerical analysis is to control properly the second order nonlinear chemotaxis term as well as to obtain a discrete energy estimate which, in particular, gives a bounded energy; this energy estimate is derived by using a regularization technique. Finally, we present some numerical simulations which allow us to validate the theoretical results obtained. [ABSTRACT FROM AUTHOR]

It is of great significance for the optimization of transportation strategy to study the methods of energy shipping scheduling. Based on the Hopfield neural network (HNN) theory, this paper proposes Hopfield neural network energy transportation path optimization algorithm with improved activation function, which solves the problems of poor mapping ability, low flexibility and high sensitivity of neurons near zero to input of traditional activation function. The improved activation function can reduce the derivative value of the activation function and the sensitivity of neurons near zero to the input value by flexibly adjusting the steepness, positioning and mapping range of energy sea transportation at the same time. The experimental results show that: under the same initial conditions, the model proposed in this paper shows better error code performance, and the data length of the required transmission sequence is shorter. When sending 8PSK (Phase Shift Keying) signal with a data length of N = 40, the error rate of the 2-path synthesized random channel is less than 0.112. The error code performance and convergence speed of the energy shipping path planning algorithm are improved effectively. [ABSTRACT FROM AUTHOR]

• This paper studies the stabilization of nonlinear time-delay systems under flexible delayed impulsive control. • It is shown that the size of delay in continuous dynamics can be smaller or bigger than the impulsive intervals. • It removes the restriction on the magnitude relationship between the delay in continuous flow and the impulsive delay. • The rate coefficients are flexible and the impulsive delay can be integrated to guarantee the stabilization of impulses. • The synchronization of chaotic neural network is formalized in terms of linear matrix inequalities. This paper studies the stabilization of nonlinear time-delay systems under flexible delayed impulsive control. Some sufficient conditions are provided for establishing stability property in terms of exponential Lyapunov-Razumikhin functions. It is shown that the size of delay in continuous dynamics can be flexible. Specially, it can be smaller or larger than the impulsive intervals, and there is no magnitude relationship between the delay in continuous flow and impulsive delay. In most existing results, from the impulsive control point of view, the Lyapunov functions were based on the assumption that there was a common threshold at every impulse point. In this study, utilizing the proposed method of average impulsive estimation (AIE), the rate coefficients are flexible, and the impulsive delay can be integrated to guarantee the effect of stabilization of impulses. As an application, the theoretical results are applied to the synchronization of a chaotic neural network, and the impulsive control input is formalized in terms of linear matrix inequalities (LMIs). The efficiency of the derived results is illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]

• This paper studies the leader-following flocking problem of the unmanned aerial vehicle (UAV). • It employs hybrid event-triggered control and pinning mechanism with delayed control inputs. • Criteria on flocking stability and Zeno behaviour prevention are derived. • It combines both displacement-based control and gyroscopic forces. • The tolerance of network instability in terms of continuous part is increased. This paper studies the leader-following flocking control problem of unmanned aerial vehicle (UAV) systems by integrating a hybrid impulsive framework, where the full exchange of information only occurs at each impulsive time instant. It is also shown that the overall stability can be achieved via impulses while the continuous dynamics remains destabilizing. Meanwhile, the even-triggered and pinning mechanisms are considered to further reduce control resource usage and transmission redundancy. Moreover, topology switching and strong nonlinearity are taken into account for more practical application. Based on transmission topology structure, impulsive control theory, and Lyapunov based event-triggered strategy, some improved theorems are derived to guarantee convergence of the corresponding error dynamics without exhibiting Zeno behaviour. Compared with most existing results on continuous or impulsive systems, the obtained stability criteria are more general as they are applicable to systems involving both delayed coupling feedback and delayed impulses. In addition, a novel approach using braking and gyroscopic forces is utilized for collision avoidance purposes. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

The exponential stabilization of stochastic neural networks in mean square sense with saturated impulsive input is investigated in this paper. Firstly, the saturated term is handled by polyhedral representation method. When the impulsive sequence is determined by average impulsive interval, impulsive density and mode-dependent impulsive density, the sufficient conditions for stability are proposed, respectively. Then, the ellipsoid and the polyhedron are used to estimate the attractive domain, respectively. By transforming the estimation of the attractive domain into a convex optimization problem, a relatively optimum domain of attraction is obtained. Finally, a three-dimensional continuous time Hopfield neural network example is provided to illustrate the effectiveness and rationality of our proposed theoretical results. • The impulsive control sequence is defined by (mode-dependent) impulsive density. • Estimating attractive domain's size is converted into solving optimization problems. • Introduce a convex set to handle mode-dependent saturated impulsive input strategies. [ABSTRACT FROM AUTHOR]

This paper investigates the cluster synchronization of coupled neural networks with reaction–diffusion terms. With the help of impulsive control strategies, some cluster synchronization criteria are proposed by an appropriate event-triggered mechanism. A numerical example is given to verify the validity of the theoretical results. Additionally, the proposed event-triggered impulsive synchronization is successfully applied to image encryption with encouraging cryptanalysis results demonstrating its strong ability to efficiently encrypt images. [ABSTRACT FROM AUTHOR]

This paper is concerned with non-fragile output-feedback control for time-delay neural networks with persistent dwell time (PDT) switching in a continuous-time setting. The main purpose is to design an output-feedback controller subject to gain fluctuations, guaranteeing both asymptotic stability and L 2 -gain of the closed-loop control system. To achieve reduced conservatism, the controller is formulated to depend not only on the system mode but also on a time scheduler constructed based on the PDT switching rule and minimum time span. A criterion for the asymptotic stability and L 2 -gain analysis is established through the application of the Gronwall–Bellman inequality and mathematical induction. Then, a numerically tractable design approach for the desired controller is proposed, utilizing a four-section piecewise time-dependent Lyapunov–Krasovskii functional and several nonlinearity decoupling techniques. For comparative purposes, a simple case, independent of the time scheduler, is also investigated, and the corresponding controller design approach is presented. Finally, a simulation example is given to illustrate the effectiveness and superiority of the proposed system mode and time scheduler dual-dependent controller design approach. [ABSTRACT FROM AUTHOR]

This paper proposes a new angular velocity observer for attitude tracking of spacecraft based on contraction analysis. The observer is designed in the inertial reference frame via estimating the inertial angular momentum to avoid the square term of the angular velocity when the spacecraft dynamics is expressed in the body frame. It employs a continuous angular-velocity dependent innovation term generated by means of a simple first-order linear filter, instead of a discontinuous attitude-dependent innovation term commonly used in angular velocity observer designs, resulting in a smooth behavior. The global exponential convergence is achieved. Moreover, when combined with the exponentially convergent tracking controller devised in this paper, it gives an overall system with exponential stability relying on a separation property. Finally, a switching function with hysteresis is introduced to stabilize the closest equilibrium in the configuration space, achieving the global exponential stability. Numerical simulations are included to illustrate the performance of the proposed observer in the closed loop, comparison with similar results, and robustness verification under inertia parameter uncertainties and noisy measurements. • A novel angular velocity observer with separation property is designed. • Global exponential convergence is shown for the proposed observer, relaying on contraction analysis. • Two attitude tracking controllers are developed in a controller-observer scheme, resulting in an overall convergent system in view of the contraction of hierarchical systems. • The separation property and robustness of the proposed controller-observer schemes are analyzed and illustrated through numerical simulations. [ABSTRACT FROM AUTHOR]

The issue of H ∞ /passive master–slave synchronization for Markov jumping neural networks with reaction–diffusion terms is investigated in this paper via an event-triggered control scheme under deception attacks. To lighten the burden of limited communication bandwidth as well as ensure the control performance, an event-triggered transmission scheme is developed. Meanwhile, the randomly occurring deception attacks, which received from the event generator are assumed to modify the sign of the control signal, are taken into account. Furthermore, sufficient conditions ensuring the prescribed H ∞ /passive performance level of the neural networks, are deduced beyond Lyapunov stability theory, and the controller gains are derived dealing with the matrix convex optimization problem. At last, the availability of the approach proposed is demonstrated via a numerical example. • Different from references (Dharani et al., 2017; Wang et al., 2021), this paper considers RDTs and parameter uncertainty. • The random deception attacks is considered. ETTS is used to save bandwidth resources. • By using LKF and inequalities, the H ∞ /passive synchronization performance is achieved. [ABSTRACT FROM AUTHOR]

In this paper, we extend a newly developed time-delay approach of extremum seeking (ES) from quadratic maps to general nonlinear maps, which substantially expands the scope of application of the time-delay method. The gradient-based ES in the case of single-variable and multi-variable nonlinear static maps are considered. Different from the recent literature, the time-delay method in this paper is applicable to a big family of nonlinear maps satisfying a couple of mild assumptions. By transforming the original ES system into a kind of time-delay system of neutral type, and further transforming the neutral delay differential equation into the perturbed ordinary differential equation (ODE), we provide simple inequalities that guarantee practical stability of the ES closed-loop system. With a prior knowledge about the upper bounds of the nonlinear map and its gradient and Hessian, the time-delay approach suggests a quantitative calculation on the lower bound of dither frequency and the ultimate upper bound of estimation error, which is difficult to achieve by the classical averaging method. [ABSTRACT FROM AUTHOR]

This paper investigates traffic forecasting, which attempts to forecast the future state of traffic based on historical situations. This problem has received ever-increasing attention in various scenarios and facilitated the development of numerous downstream applications such as urban planning and transportation management. However, the efficacy of existing methods remains sub-optimal due to their tendency to model temporal and spatial relationships independently, thereby inadequately accounting for complex high-order interactions of both worlds. Moreover, the diversity of transitional patterns in traffic forecasting makes them challenging to capture for existing approaches, warranting a deeper exploration of their diversity. Toward this end, this paper proposes Co njoint Spati o -Tempora l graph neural network (abbreviated as COOL), which models heterogeneous graphs from prior and posterior information to conjointly capture high-order spatio-temporal relationships. On the one hand, heterogeneous graphs connecting sequential observation are constructed to extract composite spatio-temporal relationships via prior message passing. On the other hand, we model dynamic relationships using constructed affinity and penalty graphs, which guide posterior message passing to incorporate complementary semantic information into node representations. Moreover, to capture diverse transitional properties to enhance traffic forecasting, we propose a conjoint self-attention decoder that models diverse temporal patterns from both multi-rank and multi-scale views. Experimental results on four popular benchmark datasets demonstrate that our proposed COOL provides state-of-the-art performance compared with the competitive baselines. • We explore a challenging yet practical problem: GNNs for traffic flow prediction. • Our model conjointly explores spatio-temporal relationships from both prior and posterior views. • Our model introduces a conjoint self-attention decoder that aggregates sequential representations. • Our model uses both multi-rank and multi-scale attention branches to learn representations. • Experiments on the benchmarks demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper intensively studied the finite-time (FNT) and fixed-time (FXT) synchronization issues for complex networks (CNs) with semi-Markovian switching and impulsive effect. The impulses are assumed to be independent of the semi-Markovian switching. Firstly, a unified FNT and FXT stability criterion of impulsive dynamical system with time-varying delays is extended by comparison principle. Secondly, two novel hybrid control schemes, which are composed of adaptive gain and switching state-feedback are proposed. Thirdly, by employing Kronecker product, Lyapunov-Krasovskii functional and inequality technique, FNT and FXT synchronization criteria for impulsive CNs with semi-Markovian switching are presented in a set of low-dimensional linear matrix inequalities, and the settling times are computed respectively. Finally, simulations are given to verify the proposed adaptive FNT and FXT synchronization criteria. • A unified finite/fixed-time stability criterion of impulsive system is extended. • The impulsive effect and semi-Markovian switching are considered in complex networks. • Under two hybrid controllers, the finite/fixed-time synchronization criteria are established. • The finite/fixed-time synchronization settling times are given by some concrete expressions. [ABSTRACT FROM AUTHOR]

This paper aims to study the fixed-time stabilization of a class of delayed discontinuous reaction–diffusion Cohen–Grossberg neural networks. Firstly, by providing some relaxed conditions containing indefinite functions and based on inequality techniques, a new fixed-time stability lemma is given, which can improve the traditional ones. Secondly, based on state-dependent switching laws, the periodic wave solution of the formulated networks is transformed into the periodic solution of ordinary differential system. By utilizing differential inclusions theory and coincidence theorem, the existence of periodic solutions is obtained. Thirdly, based on the new fixed-time stability lemma, the periodic solutions are stabilized at zero in a fixed-time, which is a new topic on reaction–diffusion networks. Moreover, the established criteria are all delay-dependent, which are less conservative than the previous delay-independent ones for ensuring the stabilization of delayed reaction–diffusion networks. Finally, two examples give numerical explanations of the proposed results and highlight the influence of delays. • Providing novel fixed-time stability criteria for reaction–diffusion Cohen–Grossberg neural networks. • Transforming the solution of the discontinuous RDCGNNs into periodic solution of ordinary differential systems. • Achieving the fixed-time stabilization of the discontinuous RDCGNNs via indefinite LKFs. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization control of fractional-order memristive neural networks with reaction–diffusion terms. With regard to the reaction–diffusion model, a novel processing method based on Hardy–Poincarè inequality is introduced, as a result, the diffusion terms are estimated associated with the information of the reaction–diffusion coefficients and the regional feature, which may be beneficial to obtain conditions with less conservatism. Then, based on Kakutani's fixed point theorem of set-valued maps, new testable algebraic conclusion for ensuring the existence of the system's equilibrium point is obtained. Subsequently, by means of Lyapunov stability theory, it is concluded that the resulting stabilization error system is global asymptotic/Mittag-Leffler stable with a prescribed controller. Finally, an illustrative example about is provided to show the effectiveness of the established results. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study two spectral Galerkin approximation schemes of the FitzHugh-Nagumo (FHN) neuron model for the nerve impulse propagation, which contains a small parameter perturbation and strong nonlinearity. To this end, we consider two kinds of temporal discretization by a semi-implicit Euler method and a Crank-Nicolson method, and the spatial discretization by the spectral Galerkin method for the perturbed FHN neuron model. In particular, in order to obtain the second-order approximation in time for the numerical scheme, we modify the nonlinear term f (u n) in the Crank-Nicolson spectral Galerkin (CNSG) scheme. We derive the error estimations with optimal convergence rates of the numerical solutions by the first-order semi-implicit spectral Galerkin (SISG) approximation scheme and the second-order modified CNSG (MCNSG) approximation scheme for the perturbed FHN neuron model. Finally, some numerical examples of one-dimensional and two-dimensional nonlinear FHN models with periodic boundary conditions are carried out to verify that the approximate solutions of the proposed SISG and MCNSG schemes satisfy the proved theoretical results. [ABSTRACT FROM AUTHOR]

This paper describes a new four-dimensional fractional discrete neural network with electromagnetic radiation model. In addition, the non-linear dynamics of the suggested model are examined, within the framework of commensurate, incommensurate and variable orders, through different numerical techniques such as Lyapunov exponent, phase portraits, bifurcation diagrams, and the 0–1 test method. The results imply that The behaviours of the proposed fractional discrete neural network model have rich and complex dynamical properties that are influenced by the variation of the system parameters, the commensurate order, the incommensurate order and the variable order. Moreover, the approximate entropy test and C o algorithm are carried out to measure complexity and validate the presence of chaos. Finally, nonlinear controllers are illustrated to stabilize and synchronize the proposed model. [ABSTRACT FROM AUTHOR]

This paper studies the stabilization analysis problem of a class of incommensurate fractional-order memristor-based neural networks with multiple time-varying delays (IFOMNNs-MTDs). In previously published studies of IFOMNNs-MTDs, the controller is usually designed as a general delay-independent feedback controller. Due to the simple form of the feedback controller, less system information is used and less adjustable parameters are considered, which limits the flexibility and control effect of controller. Specially, the use of delay information is insufficient in the existing results, which will make the controller insensitive to the influence of delay factors and affect the control performance. Thereby, the accurate analysis of the dynamic characteristics of IFOMNNs-MTDs by designing appropriate controller needs further study. This paper aims to propose a new delay-dependent controller to improve the stabilization analysis of IFOMNNs-MTDs. Firstly, a delay-dependent distributed controller with distributed control gain and time-delay state summation term is proposed, which accords with the transmission law of activation function weights and is helpful to consider the historical information (i.e., time delay factors) of system. Thereby, the flexibility and control effect of controller are improved by adding control parameters and improving the use of system information. Secondly, a new less-conservatism stabilization criterion of IFOMNNs-MTDs is established by using the designed controller. Moreover, the controller gain can be searched in a large range by using the established criterion. Finally, a numerical simulation is provided to verify the validity of the obtained results. [ABSTRACT FROM AUTHOR]

Physics-informed neural network (PINN) is an innovative universal function approximator which adds physical constraints to neural network to make the fitting results satisfy the physical laws better. In this paper, a physics-informed residual network (PIResNet) is proposed to solve the single-phase seepage equation without labeled data. The loss function is constructed by summarizing the residuals of the discretized seepage equation based on the finite volume method (FVM), and the boundary conditions are embedded in the PDE residuals in a "hard constraint" way. The PIResNet is simple in network structure, fast in convergence and easy to optimize. Furthermore, the convergence of the residual structure used in this paper is proved and the theoretical analysis of time complexity illustrates the computational efficiency of PIResNet. The correctness of the proposed method is proved and the experiments display that the solution time of PIResNet is reduced by more than six times compared to physics-informed convolutional neural networks (PICNN). [ABSTRACT FROM AUTHOR]

• An impulsive generalization of an SIR epidemic model is developed. • The model allows for applications of impulsive vaccination or impulsive control drug-treatments on the epidemic spreading. • The concept of practical stability with respect to h-manifolds is introduced. • Criteria for the global h-practical exponential stability are established. • The impulsive Lyapunov approach is applied. In this paper, we study an impulsively extended delayed SIR (Susceptible-Infected-Recovered) epidemic model for the spread of infectious diseases. The impulsive control model is represented by a neural network system with reaction-diffusion terms and impulses at fixed instants of time. The notion of stability of specific manifolds defined by continuous functions is introduced to the model under consideration. Using the Lyapunov impulsive approach, we derive criteria for the global practical exponential stability of the defined manifolds of solutions. Since the stability of manifolds concepts generalize the stability of separate state notions, our results are more general and they extend some existing stability results for non-impulsive and impulsive SIR epidemic models. An example is considered to show the effectiveness of our results. [ABSTRACT FROM AUTHOR]

Global asymptotic stability and synchronization are explored in this paper for fractional delayed memristive neural networks with reaction–diffusion terms (FDRDMNNs) in sense of Riemann–Liouville. First, we introduce diffusion into the existing model of fractional delayed memristive neural networks. Next, in terms of Green's theorem and inequality technique, a less conservative criterion for the asymptotic stability of FDRDMNNs is given by endowing Lyapunov direct method. Then, the appropriate pinning feedback controllers and adaptive controllers are designed to achieve the synchronization of the FDRDMNNs, and two sufficient conditions for global asymptotic synchronization are acquired. In addition, the results based on algebraic inequalities enhance some existing ones. The numerical simulations finally verify the validity of the derived results. • We research a type of fractional memristive neural networks models with diffusion. • A new stability algebraic criterion is obtained by the Lyapunov direct method. • Two synchronization conditions are gained by appropriate pinning control schemes. • Our results can be viewed as an extension of the existing ones. [ABSTRACT FROM AUTHOR]

This paper investigates the coexistence and local stability of multiple equilibrium points for a class of competitive neural networks with sigmoidal activation functions and time-varying delays, in which fractional-order derivative and state-dependent switching are involved at the same time. Some novel criteria are established to ensure that such n -neuron neural networks can have 5 m 1 ⋅ 3 m 2 total equilibrium points and 3 m 1 ⋅ 2 m 2 locally stable equilibrium points with m 1 + m 2 = n , based on the fixed-point theorem, the definition of equilibrium point in the sense of Filippov, the theory of fractional-order differential equation and Lyapunov function method. The investigation implies that the competitive neural networks with switching can possess greater storage capacity than the ones without switching. Moreover, the obtained results include the multistability results of both fractional-order switched Hopfield neural networks and integer-order switched Hopfield neural networks as special cases, thus generalizing and improving some existing works. Finally, four numerical examples are presented to substantiate the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, p th exponential stability and quasi-surely exponential stability of stochastic Hopfield neural networks driven by G -Brownian motion are investigated. Under a sublinear expectation framework, we give several lemmas related to the Halanay inequality and the Burkholder-Davis-Gundy ineqaulity. Our stability results is based on the class of the multidimensional Halanay inequalities, as well as the Burkholder-Davis-Gundy inequalities. The main originality lies in the fact that we consider Knightian uncertainty of the theory model of stochastic Hopfield neural networks. Finally, two numerical examples are presented to illustrate our new theory. [ABSTRACT FROM AUTHOR]

In the current paper, we use backward difference and local discontinuous Galerkin (BD-LDG) methods for temporal and spatial discretization of fourth-order partial integro-differential equations (PIDEs) with memory terms containing weakly singular kernels. This work provides a stability analysis of the proposed method, and at the end, by presenting some numerical experiments, we demonstrate the stability of the resulting scheme and show numerically that the optimal convergence rate is O (h k + 1) in the discrete L 2 norm. [ABSTRACT FROM AUTHOR]

This research paper conducts an investigation into the stability issue for a more general class of neutral-type Hopfield neural networks that involves multiple time delays in the states of neurons and multiple neutral delays in the time derivatives of the states of neurons. By constructing a new proper Lyapunov functional, an alternative easily verifiable algebraic criterion for global asymptotic stability of this type of Hopfield neural systems is derived. This new stability condition is entirely independent of time and neutral delays. Two instructive examples are employed to indicate that the result obtained in this paper reveals a new set of sufficient stability criteria when it is compared with the previously reported stability results. Therefore, the proposed stability result enlarges the application domain of Hopfield neural systems of neutral types. [ABSTRACT FROM AUTHOR]

In this paper, the existence, uniqueness and stability criteria of solutions for Hopfield neural networks with discrete and distributed delays (DDD HNNs) are investigated by the definitions of three kinds of generalized norm (ξ -norm). A general DDD HNN model is firstly introduced, where the discrete delays τ p q (t) are asynchronous time-varying delays. Then, { ξ , 1 } -norm, { ξ , 2 } -norm and { ξ , ∞ } -norm are successively used to derive the existence, uniqueness and stability criteria of solutions for the DDD HNNs. In the proof of theorems, special functions and assumptions are given to deal with discrete and distributed delays. Furthermore, a corollary is concluded for the existence and stability criteria of solutions. The methods given in this paper can also be used to study the synchronization and μ -stability of different DDD NNs. Finally, two numerical examples and their simulation figures are given to illustrate the effectiveness of these results. [ABSTRACT FROM AUTHOR]

In this paper, we address the stability of a broad class of discrete-time hypercomplex-valued Hopfield-type neural networks. To ensure the neural networks belonging to this class always settle down at a stationary state, we introduce novel hypercomplex number systems referred to as real-part associative hypercomplex number systems. Real-part associative hypercomplex number systems generalize the well-known Cayley–Dickson algebras and real Clifford algebras and include the systems of real numbers, complex numbers, dual numbers, hyperbolic numbers, quaternions, tessarines, and octonions as particular instances. Apart from the novel hypercomplex number systems, we introduce a family of hypercomplex-valued activation functions called B -projection functions. Broadly speaking, a B -projection function projects the activation potential onto the set of all possible states of a hypercomplex-valued neuron. Using the theory presented in this paper, we confirm the stability analysis of several discrete-time hypercomplex-valued Hopfield-type neural networks from the literature. Moreover, we introduce and provide the stability analysis of a general class of Hopfield-type neural networks on Cayley–Dickson algebras. • New hypercomplex number systems and a broad class of activation functions. • Stability analysis of discrete-time hypercomplex-valued Hopfield neural networks. • Hopfield-type neural networks on Cayley–Dickson and Clifford algebras. • Possible applications for multidimensional data processing. [ABSTRACT FROM AUTHOR]

A fault current limiter (FCL) is an economical option to limit the increased fault current levels, which may also improve the rotor angle stability. Previous studies on this topic mainly focused on the FCLs with quick recovery and concluded that the FCL improves the rotor angle stability. However, some commercially available FCLs have delayed recovery, which may pose different challenges and need to be studied. This paper studies the impact of a superconducting fault current limiter (SCFCL) with delayed recovery on transient rotor angle stability. This paper first develops an analytical understanding of the stability of a system with SCFCL using the equal area criterion. Later, time-domain simulations are employed to demonstrate the impacts of the SCFCL on the rotor angle stability of a single-machine infinite-bus system. The results show that the SCFCL with delayed recovery leads to rotor angle instability in some cases. • Identification of the adverse impact of SCFCL with delayed recovery on transient stability. • Transient stability assessment with different SCFCL technologies. • Transient stability assessment with different SCFCL parameters, locations, and fault types. [ABSTRACT FROM AUTHOR]

This paper mainly attempts to discuss lag H ∞ synchronization in multiple state or derivative coupled reaction–diffusion neural networks without and with parameter uncertainties. Firstly, we respectively propose two types of reaction–diffusion neural networks with multiple state and derivative couplings subject to parameter uncertainties. Secondly, by exploiting designed state feedback controllers, several criteria of the lag H ∞ synchronization for these two networks are developed based on Lyapunov functional and inequality techniques. Thirdly, lag H ∞ synchronization issues of these two networks are also coped with by virtue of devised adaptive control strategies. Finally, we provide two numerical examples to verify the obtained lag H ∞ synchronization criteria. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed event-triggered control design problem for networked linear time-invariant (LTI) systems with partially measurable states, in the presence of bounded external disturbances. A distributed interval observer-based event-triggered control scheme has been proposed, the main features of this scheme lie in a) designing a novel distributed interval observer to deal with the unknown states and bound disturbances problem; b) proposing a distributed feedback control method using interval estimation information, the partially measurable limitation has been solved; c) introducing a decreased time-varying function with dead-zone modification to avoid the Zeno behavior. Moreover, sufficient conditions for the stability of closed-loop systems are given in the Lyapunov sense by using matrix inequalities and transmission strategy. Finally, the uniformly ultimately bounded stability and Zeno behavior avoidance of the proposed approach have been numerically demonstrated. • A novel distributed interval observer is presented. • Distributed interval estimation is introduced in the event-triggered control design. • A sufficient stable condition is given using monotonic theory and Lyapunov stability. [ABSTRACT FROM AUTHOR]

Mining the best logical rule from the data is a challenging task because not all attribute of the dataset will contribute towards the optimal logical representation. Even if the correct attributes were selected, wrong logical connection in the logical formula will lead to suboptimal logical representation of the datasets. These two factors must be carefully considered in creating more robust logic mining method. In this paper, we proposed a novel logic mining by introducing log-linear analysis to select the best attributes which formulate the logical rule that will be embedded into the energy-based ANN named Discrete Hopfield Neural Network (DHNN). In log-linear phase, the test of the association for each attributes will be carried out where the attributes that have a significant level less than α will be selected before proceeding to the logic mining phase. By using DHNN, the selected attributes via log-linear will be learned and retrieved the optimal induced logic with classification ability. The proposed hybrid model has been tested using various real-life datasets and was compared with several established logic mining methods. Based on the findings, several winning points for the proposed model where the proposed model dominates 3 metrics out of 5 in the average rank. The metrics that achieve the highest average rank are Accuracy (1.800), Precision (3.500), and Mathews Correlation Coefficient (2.700). In accordance with the experimental result obtained, the proposed model has achieved optimal performance with a statistically significant p -value. Hence, these findings lead to an advancement of the existing logic mining via the statistical method. [ABSTRACT FROM AUTHOR]

• An attempt has been made to understand the effect of electromagnetic induction on the network of neurons. • An excitable slow-fast memristive model has been studied with its various intrinsic dynamics. • We analytically establish the existence and stability of Hopf bifurcation with bifurcating periodic solutions. • We investigate the emergence of multi-arm antispiral waves in the system with proper analytical justification. • A random network architecture is used to study the dynamics of coupled network that generates MMOs and bursting patterns. The diverse firing responses in a single neuron model as well as in a neuronal network play a major role in understanding the collective neuronal dynamics. In this paper, we consider an excitable slow-fast memristive model and study its various intrinsic dynamics by allowing a periodic external stimulus. The single model exhibits various types of spiking, bursting, mixed-mode oscillations (MMOs), and mixed-mode bursting oscillations (MMBOs) depending on the amplitude and frequency of the periodic injected current. Corresponding bifurcation analysis reveals the existence of supercritical and subcritical Hopf bifurcations in the system depending on the major predominant parameters that establish the scenarios of the neuronal responses. We have verified analytically the existence and stability of Hopf bifurcations. The memristive system can produce cascade of period doubling bifurcations for particular parameter regimes. Next, we investigate the emergence of multi-arm antispiral waves in the diffusively coupled system with proper analytical justification. We have also computed the group and phase velocities to discern the spiral and antispiral waves near the Hopf instability. A transition from target wave to multi-arm antispiral wave is observed in the diffusive system. Moreover, we use a random network architecture different from the diffusive network to study the dynamics of the coupled network for certain firing activities. It is observed that the network of heterogeneous desynchronized neurons with higher electrical couplings, can generate MMOs, MMBOs, and bursting for different external stimuli. However, the uncoupled systems cannot reveal such typical dynamics for particular parameters. Further, we introduce a reduced-order model to summarize the complete dynamics of the larger random network and report the findings. [ABSTRACT FROM AUTHOR]

Convolutional Neural Networks have achieved state-of-the-art performance in image classification. Their lack of ability to recognise the spatial relationship between features, however, leads to misclassification of the variants of the same image. Capsule Networks were introduced to address this issue by incorporating the spatial information of image features into neural networks. In this paper, we are interested in showcasing the digit recognition task on CAPTCHA images, widely considered a challenge for computers in relation to human capabilities. Our intention is to provide a rigorous empirical regime in which we can compare the competitive performance of Capsule Networks against the Convolutional Neural Networks. Indeed since CAPTCHA distorts images, by adjusting the spatial positioning of features, we aim to demonstrate the advantages and limitations of Capsule Networks architecture. We train the Capsule Networks with Dynamic Routing version and the convolutional-neural-network-based deep-CAPTCHA baseline model to predict the digit sequences on numerical CAPTCHAs, investigate the performance results and propose two improvements to the Capsule Networks model. [ABSTRACT FROM AUTHOR]

In order to solve a challenging problem, i.e., fixed time synchronization of bilayer networks with derivative coupling and nonlinear delay coupling, fixed time polices are brought to achieve random synchronization for bilayer multiple weight hybrid coupled networks of neuron nodes. Being different from the synthesis method, which is often used to get theoretical conclusions from known conditions for synchronization of networks in general articles, analysis method is applied to seek parameters in fixed time controllers and sufficient conditions for synchronization from conclusions. After analysis, we obtain a relationship between coefficients of controllers and coefficients of a formula which is related to Lyapunov function. Moreover, we find that fixed settling time for synchronization is affected by the maximum eigenvalue of a matrix associated with network topology, parameters in the designed controllers and the size of networks. Finally, synchronous tests of bilayer networks of Hindmarsh–Rose (HR) neuron nodes are carried out to show the effectiveness of theoretical results. • We construct models of bilayer multi-weighted stochastic networks with neuron nodes, which are composed of multiple derivative and nonlinear delay coupling. • In this paper, fixed time controllers are designed. Parameters of fixed time controllers and sufficient criteria of synchronization are obtained via analysis method, which is to seek parameters in fixed time controllers and sufficient conditions for synchronization from the conclusion. This is different from many previous works. • A relationship between some coefficients of fixed time controllers and the coefficients of a formula which is related to Lyapunov function is given. • We find that fixed settling time is affected by maximum eigenvalue of the matrix which is related to network topologies, parameters in the designed controllers and nodes of networks. [ABSTRACT FROM AUTHOR]

Recently, solving differential equations by deep neural networks has attracted lots of attention, however, when the solution of differential equations has localized areas such as the rogue waves, the classical physics-informed neural networks (PINNs) cannot guarantee its prediction accuracy. In this paper, we propose two neural networks methods: mix-training physics-informed neural networks (MTPINNs) and prior information mix-training physics-informed neural networks (PMTPINNs), two deep learning models with more approximation ability based on PINNs. A series of numerical experiments show that the learning efficiency and absolute error accuracy of our proposed model can be improved significantly. The PMTPINNs model can so as to make up for the shortcomings of PINNs in this aspect. Furthermore, by testing the robustness of these two methods, for two kinds of rogue waves of the Hirota equation, it is surprising that these models also have good performance and thereby may provide more possibilities for solving mathematical physics problems better. • Two neural networks methods have been proposed to study the high-order rogue waves of the Hirota equation. • The MTPINNs and the PMTPINNs yield considerable improvement in accuracy and have good robustness. • We propose the adjusted PMTPINNs+, which further improves the learning and prediction ability of PMTPINNs. [ABSTRACT FROM AUTHOR]