Multimodel Integrated Enterprise Credit Evaluation Method Based on Attention Mechanism.

Due to the difficulty of credit risk assessment, the current financing and loan difficulties of small- and medium-sized enterprises (SMEs) are particularly prominent, which hinders the operation and development of enterprises. Based on the previous researches, this paper first screens out features by correlation coefficient method and gradient boosting decision tree (GBDT). Then, with the help of SE-Block, the attention mechanism is added to the feature tensor of the subset separated from metadata. On this foundation, two models, XGBoost and LightGBM, are used to train four subsets, respectively, and Bayesian ridge regression is used to fuse the training results of single models under different subsets. In the simulation experiment, the AUC value of the NN-ATT-Bayesian-Stacking model reaches 0.9675 and the distribution of prediction results is ideal. The model shows good robustness, which could make a reliable assessment for the financing and loans of SMEs.

Passive filter design for fractional-order quaternion-valued neural networks with neutral delays and external disturbance.

The problem on passive filter design for fractional-order quaternion-valued neural networks (FOQVNNs) with neutral delays and external disturbance is considered in this paper. Without separating the FOQVNNs into two complex-valued neural networks (CVNNs) or the FOQVNNs into four real-valued neural networks (RVNNs), by constructing Lyapunov-Krasovskii functional and using inequality technique, the delay-independent and delay-dependent sufficient conditions presented as linear matrix inequality (LMI) to confirm the augmented filtering dynamic system to be stable and passive with an expected dissipation are derived. One numerical example with simulations is furnished to pledge the feasibility for the obtained theory results.

Existence and finite-time stability of discrete fractional-order complex-valued neural networks with time delays.

Without decomposing complex-valued systems into real-valued systems, the existence and finite-time stability for discrete fractional-order complex-valued neural networks with time delays are discussed in this paper. First of all, in order to obtain the main results, a new discrete Caputo fractional difference equation is proposed in complex field based on the theory of discrete fractional calculus, which generalizes the fractional-order neural networks in the real domain. Additionally, by utilizing Arzela-Ascoli's theorem, inequality scaling skills and fixed point theorem, some sufficient criteria of delay-dependent are deduced to ensure the existence and finite-time stability of solutions for proposed networks. Finally, the validity and feasibility of the derived theoretical results are indicated by two numerical examples with simulations. Furthermore, we have drawn the following facts: with the lower order, the discrete fractional-order complex-valued neural networks will achieve the finite-time stability more easily.

A waiting-time-based event-triggered scheme for stabilization of complex-valued neural networks.

This paper addresses the global stabilization of complex-valued neural networks (CVNNs) via event-triggered control. First, a waiting-time-based event-triggered scheme is designed to reduce the data transmission rate. Therein, an exponential decay term is introduced into the predefined threshold function, which may postpone the triggering instant of the necessary data and therefore reduce the frequency of data transmission. Then, with the help of the input delay approach, a time-dependent piecewise-defined Lyapunov-Krasovskii functional is constructed for closed-loop system to formulate a less conservative stability criterion. In addition, by resorting to matrix transformation, the co-design method for both the feedback gains and the trigger parameters is derived. Finally, a numerical example is given to illustrate the feasibility and superiority of the proposed event-triggered scheme and the obtained theoretical results.

Global Mittag-Leffler stability and synchronization of discrete-time fractional-order complex-valued neural networks with time delay.

Without decomposing complex-valued systems into real-valued systems, this paper investigates existence, uniqueness, global Mittag-Leffler stability and global Mittag-Leffler synchronization of discrete-time fractional-order complex-valued neural networks (FCVNNs) with time delay. Inspired by Lyapunov's direct method on continuous-time systems, a class of discrete-time FCVNNs is further discussed by employing the fractional-order extension of Lyapunov's direct method. Firstly, by means of contraction mapping theory and Cauchy's inequality, a sufficient condition is presented to ascertain the existence and uniqueness of the equilibrium point for discrete-time FCVNNs. Then, based on the theory of discrete fractional calculus, discrete Laplace transform, the theory of complex functions and discrete Mittag-Leffler functions, a sufficient condition is established for global Mittag-Leffler stability of the proposed networks. Additionally, by applying the Lyapunov's direct method and designing a effective control scheme, the sufficient criterion is derived to ensure the global Mittag-Leffler synchronization of discrete-time FCVNNs. Finally, two numerical examples are also presented to manifest the feasibility and validity of the obtained results.

Novel bifurcation results for a delayed fractional-order quaternion-valued neural network.

This paper reports the innovative results on the stability and bifurcation for a delayed fractional-order quaternion-valued neural network(FOQVNN). Delay-stimulated bifurcation criteria of the developed FOQVNN are attained. Then, the bifurcation diagrams are perfectly exhibited to authenticate the veracity of the bifurcation results. Besides, the stability zone is more larger of the addressed FOQVNN in comparison with its counterpart if other parameters are intercalated. It further witnesses that the amplitudes of bifurcation oscillation get bigger with the augmentation of time delay. It discloses that the bifurcation phenomena engender earlier as the order incrementally magnifies. The exactness and merits of the achieved analytic results are eventually substantiated by a simulation example.

Effects of State-Dependent Impulses on Robust Exponential Stability of Quaternion-Valued Neural Networks Under Parametric Uncertainty.

This paper addresses the state-dependent impulsive effects on robust exponential stability of quaternion-valued neural networks (QVNNs) with parametric uncertainties. In view of the noncommutativity of quaternion multiplication, we have to separate the concerned quaternion-valued models into four real-valued parts. Then, several assumptions ensuring every solution of the separated state-dependent impulsive neural networks intersects each of the discontinuous surface exactly once are proposed. In the meantime, by applying the B -equivalent method, the addressed state-dependent impulsive models are reduced to fixed-time ones, and the latter can be regarded as the comparative systems of the former. For the subsequent analysis, we proposed a novel norm inequality of block matrix, which can be utilized to analyze the same stability properties of the separated state-dependent impulsive models and the reduced ones efficaciously. Afterward, several sufficient conditions are well presented to guarantee the robust exponential stability of the origin of the considered models; it is worth mentioning that two cases of addressed models are analyzed concretely, that is, models with exponential stable continuous subsystems and destabilizing impulses, and models with unstable continuous subsystems and stabilizing impulses. In addition, an application case corresponding to the stability problem of models with unstable continuous subsystems and stabilizing impulses for state-dependent impulse control to robust exponential synchronization of QVNNs is considered summarily. Finally, some numerical examples are proffered to illustrate the effectiveness and correctness of the obtained results.

Multistability Analysis of Quaternion-Valued Neural Networks With Time Delays.

This paper addresses the multistability issue for quaternion-valued neural networks (QVNNs) with time delays. By using the inequality technique, sufficient conditions are proposed for the boundedness and the global attractivity of delayed QVNNs. Based on the geometrical properties of the activation functions, several criteria are obtained to ensure the existence of equilibrium points, of which are locally stable. Two numerical examples are provided to illustrate the effectiveness of the obtained results.

Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons.

This paper talks about the stability and synchronization problems of fractional-order quaternion-valued neural networks (FQVNNs) with linear threshold neurons. On account of the non-commutativity of quaternion multiplication resulting from Hamilton rules, the FQVNN models are separated into four real-valued neural network (RVNN) models. Consequently, the dynamic analysis of FQVNNs can be realized by investigating the real-valued ones. Based on the method of M-matrix, the existence and uniqueness of the equilibrium point of the FQVNNs are obtained without detailed proof. Afterwards, several sufficient criteria ensuring the global Mittag-Leffler stability for the unique equilibrium point of the FQVNNs are derived by applying the Lyapunov direct method, the theory of fractional differential equation, the theory of matrix eigenvalue, and some inequality techniques. In the meanwhile, global Mittag-Leffler synchronization for the drive-response models of the addressed FQVNNs are investigated explicitly. Finally, simulation examples are designed to verify the feasibility and availability of the theoretical results.

Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties.

In this paper, the boundedness and robust stability for a class of delayed complex-valued neural networks with interval parameter uncertainties are investigated. By using Homomorphic mapping theorem, Lyapunov method and inequality techniques, sufficient condition to guarantee the boundedness of networks and the existence, uniqueness and global robust stability of equilibrium point is derived for the considered uncertain neural networks. The obtained robust stability criterion is expressed in complex-valued LMI, which can be calculated numerically using YALMIP with solver of SDPT3 in MATLAB. An example with simulations is supplied to show the applicability and advantages of the acquired result.

Stability Analysis of Continuous-Time and Discrete-Time Quaternion-Valued Neural Networks With Linear Threshold Neurons.

This paper addresses the problem of stability for continuous-time and discrete-time quaternion-valued neural networks (QVNNs) with linear threshold neurons. Applying the semidiscretization technique to the continuous-time QVNNs, the discrete-time analogs are obtained, which preserve the dynamical characteristics of their continuous-time counterparts. Via the plural decomposition method of quaternion, homeomorphic mapping theorem, as well as Lyapunov theorem, some sufficient conditions on the existence, uniqueness, and global asymptotical stability of the equilibrium point are derived for the continuous-time QVNNs and their discrete-time analogs, respectively. Furthermore, a uniform sufficient condition on the existence, uniqueness, and global asymptotical stability of the equilibrium point is obtained for both continuous-time QVNNs and their discrete-time version. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.

Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties.

This paper addresses the problem of robust stability for quaternion-valued neural networks (QVNNs) with leakage delay, discrete delay and parameter uncertainties. Based on Homeomorphic mapping theorem and Lyapunov theorem, via modulus inequality technique of quaternions, some sufficient conditions on the existence, uniqueness, and global robust stability of the equilibrium point are derived for the delayed QVNNs with parameter uncertainties. Furthermore, as direct applications of these results, several sufficient conditions are obtained for checking the global robust stability of QVNNs without leakage delay as well as complex-valued neural networks (CVNNs) with both leakage and discrete delays. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.

Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects.

In this paper, the global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects is discussed. By employing Lyapunov functional method and using matrix inequality technique, several sufficient conditions in complex-valued linear matrix inequality form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the considered neural networks. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The proposed stability results are less conservative than some recently known ones in the literatures, which is demonstrated via two examples with simulations.

Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays.

This paper investigates the stability problem for a class of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. By employing the idea of vector Lyapunov function, M-matrix theory and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of equilibrium point. When the impulsive effects are not considered, several sufficient conditions are also given to guarantee the existence, uniqueness and global exponential stability of equilibrium point. Two examples are given to illustrate the effectiveness and lower level of conservatism of the proposed criteria in comparison with some existing results.

Global dissipativity analysis on uncertain neural networks with mixed time-varying delays.

In this paper, the problems of global dissipativity and global exponential dissipativity are investigated for uncertain neural networks with discrete time-varying delay and distributed time-varying delay as well as general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing Newton-Leibniz formulation and linear matrix inequality (LMI) technique, several new criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in terms of LMI, which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness and decreased conservatism of the proposed criteria in comparison with some existing results. It is noteworthy that the traditional assumptions on the differentiability of the time-varying delays and the boundedness of its derivative are removed.

Stability analysis of impulsive Cohen-Grossberg neural network with unbounded discrete time-varying delays.

In this paper, the impulsive Cohen-Grossberg neural network with unbounded discrete time-varying delays is considered. By using the analysis method and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of the addressed neural network. These results generalize the existing relevant stability results. Two examples with simulations are given to show the effectiveness of the obtained results.

Impulsive effects on stability of fuzzy Cohen-Grossberg neural networks with time-varying delays.

In this correspondence, the impulsive effects on the stability of fuzzy Cohen-Grossberg neural networks (FCGNNs) with time-varying delays are considered. Several sufficient conditions are obtained ensuring global exponential stability of equilibrium point for the neural networks by the idea of vector Lyapunov function, M-matrix theory, and analytic methods. Moreover, the estimation for exponential convergence rate index is proposed. The obtained results not only show that the stability still remains under certain impulsive perturbations for the continuous stable FCGNNs with time-varying delays, but also present an approach to stabilize the unstable FCGNNs with time-varying delays by utilizing impulsive effects. An example with simulations is given to show the effectiveness of the obtained results.