Global asymptotic stability of complex-valued neural networks with additive time-varying delays

In this paper, we extensively study the global asymptotic stability problem of complex-valued neural networks with leakage delay and additive time-varying delays. By constructing a suitable Lyapunov–Krasovskii functional and applying newly developed complex valued integral inequalities, sufficient conditions for the global asymptotic stability of proposed neural networks are established in the form of complex-valued linear matrix inequalities. This linear matrix inequalities are efficiently solved by using standard available numerical packages. Finally, three numerical examples are given to demonstrate the effectiveness of the theoretical results.     

The uniqueness theorem for complex-valued neural networks with threshold parameters and the redundancy of the parameters

This paper will prove the uniqueness theorem for 3-layered complex-valued neural networks where the threshold parameters of the hidden neurons can take non-zeros. That is, if a 3-layered complex-valued neural network is irreducible, the 3-layered complex-valued neural network that approximates a given complex-valued function is uniquely determined up to a finite group on the transformations of the learnable parameters of the complex-valued neural network.     

Design of delay-dependent state estimator for discrete-time recurrent neural networks with interval discrete and infinite-distributed time-varying delays

The state estimation problem for discrete-time recurrent neural networks with both interval discrete and infinite-distributed time-varying delays is studied in this paper, where interval discrete time-varying delay is in a given range. The activation functions are assumed to be globally Lipschitz continuous. A delay-dependent condition for the existence of state estimators is proposed based on new bounding techniques. Via solutions to certain linear matrix inequalities, general full-order state estimators are designed that ensure globally asymptotic stability. The significant feature is that no inequality is needed for seeking upper bounds for the inner product between two vectors, which can reduce the conservatism of the criterion by employing the new bounding techniques. Two illustrative examples are given to demonstrate the effectiveness and applicability of the proposed approach.     

Models of Hopfield-type quaternion neural networks and their energy functions

Recently models of neural networks that can directly deal with complex numbers, complex-valued neural networks, have been proposed and several studies on their abilities of information processing have been done. Furthermore models of neural networks that can deal with quaternion numbers, which is the extension of complex numbers, have also been proposed. However they are all multilayer quaternion neural networks. This paper proposes models of fully connected recurrent quaternion neural networks, Hopfield-type quaternion neural networks. Since quaternion numbers are non-commutative on multiplication, some different models can be considered. We investigate dynamics of these proposed models from the point of view of the existence of an energy function and derive their conditions for existence.     

Global and robust stability of interval Hopfield neural networks with time-varying delays

In this paper, we investigate the problem of global and robust stability of a class of interval Hopfield neural networks that have time-varying delays. Some criteria for the global and robust stability of such networks are derived, by means of constructing suitable Lyapunov functionals for the networks. As a by-product, for the conventional Hopfield neural networks with time-varying delays, we also obtain some new criteria for their global and asymptotic stability.     

Mean square exponential and robust stability of stochastic discrete-time genetic regulatory networks with uncertainties

This paper aims to analyze global robust exponential stability in the mean square sense of stochastic discrete-time genetic regulatory networks with stochastic delays and parameter uncertainties. Comparing to the previous research works, time-varying delays are assumed to be stochastic whose variation ranges and probability distributions of the time-varying delays are explored. Based on the stochastic analysis approach and some analysis techniques, several sufficient criteria for the global robust exponential stability in the mean square sense of the networks are derived. Moreover, two numerical examples are presented to show the effectiveness of the obtained results.     

一类具变时滞的模糊BAM神经网络的平衡点的指数稳定性(英文)

研究一类具变时滞的模糊BAM神经网络.利用拓扑度论和微分不等式,获得了该类网络平衡点的存在性、唯一性和全局指数稳定性的充分条件.一个例子用来解释本文获得的结果.     

Stability of delayed memristive neural networks with time-varying impulses

This paper addresses the stability problem on the memristive neural networks with time-varying impulses. Based on the memristor theory and neural network theory, the model of the memristor-based neural network is established. Different from the most publications on memristive networks with fixed-time impulse effects, we consider the case of time-varying impulses. Both the destabilizing and stabilizing impulses exist in the model simultaneously. Through controlling the time intervals of the stabilizing and destabilizing impulses, we ensure the effect of the impulses is stabilizing. Several sufficient conditions for the globally exponentially stability of memristive neural networks with time-varying impulses are proposed. The simulation results demonstrate the effectiveness of the theoretical results.     

Synchronization criteria of discrete-time complex networks with time-varying delays and parameter uncertainties

This paper is pertained with the synchronization problem for an array of coupled discrete-time complex networks with the presence of both time-varying delays and parameter uncertainties. The time-varying delays are considered both in the network couplings and dynamical nodes. By constructing suitable Lyapunov–Krasovskii functional and utilizing convex reciprocal lemma, new synchronization criteria for the complex networks are established in terms of linear matrix inequalities. Delay-partitioning technique is employed to incur less conservative results. All the results presented here not only depend upon lower and upper bounds of the time-delay, but also the number of delay partitions. Numerical simulations are rendered to exemplify the effectiveness and applicability of the proposed results.     

Analyzing inner and outer synchronization between two coupled discrete-time networks with time delays

This paper studies two kinds of synchronization between two discrete-time networks with time delays, including inner synchronization within each network and outer synchronization between two networks. Based on Lyapunov stability theory and linear matrix inequality (LMI), sufficient conditions for two discrete-time networks to be asymptotic stability are derived in terms of LMI. Finally numerical examples are given to illustrate the effectiveness of our derived results. The theoretical understanding provides insights into the dynamics of two or more neural networks with appropriate couplings.     

Mean square stability of uncertain stochastic BAM neural networks with interval time-varying delays

The robust asymptotic stability analysis for uncertain BAM neural networks with both interval time-varying delays and stochastic disturbances is considered. By using the stochastic analysis approach, employing some free-weighting matrices and introducing an appropriate type of Lyapunov functional which takes into account the ranges for delays, some new stability criteria are established to guarantee the delayed BAM neural networks to be robustly asymptotically stable in the mean square. Unlike the most existing mean square stability conditions for BAM neural networks, the supplementary requirements that the time derivatives of time-varying delays must be smaller than 1 are released and the lower bounds of time varying delays are not restricted to be 0. Furthermore, in the proposed scheme, the stability conditions are delay-range-dependent and rate-dependent/independent. As a result, the new criteria are applicable to both fast and slow time-varying delays. Three numerical examples are given to illustrate the effectiveness of the proposed criteria.     

Passivity of memristor-based BAM neural networks with different memductance and uncertain delays

This paper addresses the passivity problem for a class of memristor-based bidirectional associate memory (BAM) neural networks with uncertain time-varying delays. In particular, the proposed memristive BAM neural networks is formulated with two different types of memductance functions. By constructing proper Lyapunov–Krasovskii functional and using differential inclusions theory, a new set of sufficient condition is obtained in terms of linear matrix inequalities which guarantee the passivity criteria for the considered neural networks. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theoretical results.     

Synchronization of chaotic nonlinear continuous neural networks with time-varying delay

In this paper, the synchronization problem for delayed continuous time nonlinear complex neural networks is considered. The delay dependent state feed back synchronization gain matrix is obtained by considering more general case of time-varying delay. Using Lyapunov stability theory, the sufficient synchronization criteria are derived in terms of Linear Matrix Inequalities (LMIs). By decomposing the delay interval into multiple equidistant subintervals, Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Employing these LKFs, new delay dependent synchronization criteria are proposed in terms of LMIs for two cases with and without derivative of time-varying delay. Numerical examples are illustrated to show the effectiveness of the proposed method.     

Exponential input-to-state stability of recurrent neural networks with multiple time-varying delays

In this paper, input-to-state stability problems for a class of recurrent neural networks model with multiple time-varying delays are concerned with. By utilizing the Lyapunov–Krasovskii functional method and linear matrix inequalities techniques, some sufficient conditions ensuring the exponential input-to-state stability of delayed network systems are firstly obtained. Two numerical examples and its simulations are given to illustrate the efficiency of the derived results.     

Robust exponential stabilization of a class of delayed neural networks with reaction-diffusion terms

In this paper, the problem of global robust exponential stabilization for a class of neural networks with reaction-diffusion terms and time-varying delays which covers the Hopfield neural networks and cellular neural networks is investigated. A feedback control gain matrix is derived to achieve the global robust exponential stabilization of the neural networks by using the Lyapunov stability theory, and the stabilization condition can be verified if a certain Hamiltonian matrix with no eigenvalues on the imaginary axis. This condition can avoid solving an algebraic Riccati equation. Finally, a numerical simulation illustrates the effectiveness of the results.     

New stability criterion of neural networks with leakage delays and impulses: a piecewise delay method

This paper analyzes the global asymptotic stability of a class of neural networks with time delay in the leakage term and time-varying delays under impulsive perturbations. Here the time-varying delays are assumed to be piecewise. In this method, the interval of the variation is divided into two subintervals by its central point. By developing a new Lyapunov–Krasovskii functional and checking its variation in between the two subintervals, respectively, and then we present some sufficient conditions to guarantee the global asymptotic stability of the equilibrium point for the considered neural network. The proposed results which do not require the boundedness, differentiability and monotonicity of the activation functions, can be easily verified via the linear matrix inequality (LMI) control toolbox in MATLAB. Finally, a numerical example and its simulation are given to show the conditions obtained are new and less conservative than some existing ones in the literature.     

变时延神经网络的全局指数稳定性及收敛性

利用Lyapunov泛函方法和线性矩阵不等式（LMI）技术,通过引入一系列参数,给出全局指数稳定的平衡点的判别条件和时延的最大上界和神经网络的收敛速度,所得结果较之一些文献中的结果简单、实用并且对于具体设计带时延神经网络有重要的指导意义.最后,通过实例表明给出的判定条件是有效、可行的.     

Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays

This paper investigates the finite-time synchronization and fixed-time synchronization problems of inertial memristive neural networks with time-varying delays. By utilizing the Filippov discontinuous theory and Lyapunov stability theory, several sufficient conditions are derived to ensure finite-time synchronization of inertial memristive neural networks. Then, for the purpose of making the setting time independent of initial condition, we consider the fixed-time synchronization. A novel criterion guaranteeing the fixed-time synchronization of inertial memristive neural networks is derived. Finally, three examples are provided to demonstrate the effectiveness of our main results.     

Robust exponential stability of markovian jumping neural networks with time-varying delay

This paper considers the robust stability of a class of neural networks with Markovian jumping parameters and time-varying delay. By employing a new Lyapunov-Krasovskii functional, a sufficient condition for the global exponential stability of the delayed Markovian jumping neural networks is established. The proposed condition is also extended to the uncertain cases, which are shown to be the improvement and extension of the existing ones. Finally, the validity of the results are illustrated by an example.     

具有分布时滞离散Cohen-Grossberg神经网络的周期解

讨论了一类具有分布时滞离散Cohen-Grossberg神经网络模型,利用M-矩阵理论与适合的Lypunov函数,得到该类模型周期解的存在性与全局指数稳定性．