Stability analysis of impulsive Cohen–Grossberg neural networks with distributed delays and reaction–diffusion terms

In this paper, we investigate a class of impulsive Cohen–Grossberg neural networks with distributed delays and reaction–diffusion terms. By establishing an integro-differential inequality with impulsive initial conditions and applying M-matrix theory, we find some sufficient conditions ensuring the existence, uniqueness, global exponential stability and global robust exponential stability of equilibrium point for impulsive Cohen–Grossberg neural networks with distributed delays and reaction–diffusion terms. An example is given to illustrate the results obtained here.     

Stability analysis of the zero solution for two class evolution equations

By constructing some suitable Lyapunov-type functionals and applying the theory of the definite-quadratic form, we obtain the stability of the zero solution of two classes of evolution equations with delays, including reaction–diffusion equations and damped wave equations. Our criteria depend on the derivatives of delays. Consequently, when the delays are constants, these criteria are independent of the magnitudes of the delays, so the delays are harmless for the stability of the zero solution.     

带有时滞的Clifford值神经网络的全局指数稳定性

研究了带有离散时滞和分布时滞的Clifford值递归神经网络的全局指数稳定性问题.首先运用M矩阵的性质和不等式技巧证明了Clifford值递归神经网络平衡点的存在性和唯一性;然后通过数学分析方法,得到了Clifford值递归神经网络全局指数稳定的判定条件;最后数值仿真例子验证了获得结果的有效性.     

Exponential stability for stochastic BAM networks with discrete and distributed delays

In this paper, we investigate exponential stability for stochastic BAM networks with mixed delays. The mixed delays include discrete and distributed time-delays. The purpose of this paper is to establish some criteria to ensure the delayed stochastic BAM neural networks are exponential stable in the mean square. A sufficient condition is established by consructing suitable Lyapunov functionals. The condition is expressed in terms of the feasibility to a couple LMIs. Therefore, the exponential stability of the stochastic BAM networks with discrete and distributed delays can be easily checked by using the numerically efficient Matlab LMI toobox. A simple example is given to demonstrate the usefulness of the derived LMI-based stability conditions.     

Lasalle method and general decay stability of stochastic neural networks with mixed delays

This paper investigates the general decay pathwise stability conditions on a class of stochastic neural networks with mixed delays by applying Lasalle method. The mixed time delays comprise both time-varying delays and infinite distributed delays. The contributions are as follows: (1)?we extend the Lasalle-type theorem to cover stochastic differential equations with mixed delays; (2)?based on the stochastic Lasalle theorem and the M-matrix theory, new criteria of general decay stability, which includes the almost surely exponential stability and the almost surely polynomial stability and the partial stability, for neural networks with mixed delays are established. As an application of our results, this paper also considers a two-dimensional delayed stochastic neural networks model.     

An LMI approach to stability analysis of stochastic high-order Markovian jumping neural networks with mixed time delays

This paper deals with the problem of global exponential stability for a general class of stochastic high-order neural networks with mixed time delays and Markovian jumping parameters. The mixed time delays under consideration comprise both discrete time-varying delays and distributed time-delays. The main purpose of this paper is to establish easily verifiable conditions under which the delayed high-order stochastic jumping neural network is exponentially stable in the mean square in the presence of both mixed time delays and Markovian switching. By employing a new Lyapunov–Krasovskii functional and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria ensuring exponential stability. Furthermore, the criteria are dependent on both the discrete time-delay and distributed time-delay, and hence less conservative. The proposed criteria can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria.     

A graph‐theoretic approach to stability of neutral stochastic coupled oscillators network with time‐varying delayed coupling

In this paper, a graph‐theoretic approach for checking exponential stability of the system described by neutral stochastic coupled oscillators network with time‐varying delayed coupling is obtained. Based on graph theory and Lyapunov stability theory, delay‐dependent criteria are deduced to ensure moment exponential stability and almost sure exponential stability of the addressed system, respectively. These criteria can show how coupling topology, time delays, and stochastic perturbations affect exponential stability of such oscillators network. This method may also be applied to other neutral stochastic coupled systems with time delays. Finally, numerical simulations are presented to show the effectiveness of theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

In this paper, the dynamic analysis problem is considered for a new class of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some asymptotic stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be easily calculated by LMI Toolbox in Matlab. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some existing results in the literature.     

Stability of Delayed Markovian Switching Stochastic Neutral-type Reaction-diffusion Neural Networks

This paper is concerned about exponential stability in mean square of Markovian switching delayed reaction-diffusion neutral-type stochastic neural networks (RNSNNs). By Lyapunov function method, several novel stability criteria on exponential mean square stability of Markovian switching RNSNNs with time-varying delays are obtained. In the end, two examples are given to verify the feasibility of our findings.     

Global exponential stability in Lagrange sense for recurrent neural networks with time delays

In this paper, we study the global exponential stability in Lagrange sense for continuous recurrent neural networks (RNNs) with multiple time delays. Three different types of activation functions are considered, which include both bounded and unbounded activation functions. By constructing appropriate Lyapunov-like functions, we provide easily verifiable criteria for the boundedness and global exponential attractivity of RNNs. These results can be applied to analyze monostable as well as multistable neural networks.     

Stability analysis in Lagrange sense for a non-autonomous Cohen–Grossberg neural network with mixed delays

The paper discusses the global exponential stability in the Lagrange sense for a non-autonomous Cohen–Grossberg neural network (CGNN) with time-varying and distributed delays. The boundedness and global exponential attractivity of non-autonomous CGNN with time-varying and distributed delays are investigated by constructing appropriate Lyapunov-like functions. Moreover, we provide verifiable criteria on the basis of considering three different types of activation function, which include both bounded and unbounded activation functions. These results can be applied to analyze monostable as well as multistable biology neural networks due to making no assumptions on the number of equilibria. Meanwhile, the results obtained in this paper are more general and challenging than that of the existing references. In the end, an illustrative example is given to verify our results.     

Exponential stability of recurrent neural networks with time-varying discrete and distributed delays

This paper is concerned with the problems of determining the global exponential stability and estimating the exponential-convergence rate for a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. By constructing an appropriate Lyapunov–Krasovskii functional and employing linear matrix inequality (LMI) technique, new delay-dependent exponential-stability criteria are derived in term of LMIs and the exponential-convergence rate is estimated. Numerical examples are given to show the effectiveness and improvement of the obtained results.     

Further results on mean square exponential stability of uncertain stochastic delayed neural networks

In this paper, the mean square exponential stability problem is deal with for a class of uncertain stochastic neural networks with time-varying delays. By introducing a new Lyapunov–Krasovskii function, improved delay-dependent stability criteria are established in term of linear matrix inequalities (LMIs). Finally, two numerical examples are given to show that our results are less conservative and more efficiency than the existing stability criteria.     

Neural networks with discrete and distributed time-varying delays: A general stability analysis

In this paper, the global asymptotic and exponential stability are investigated for a class of neural networks with both the discrete and distributed time-varying delays. By using appropriate Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique, several delay-dependent sufficient conditions are obtained to guarantee the global asymptotic and exponential stability of the addressed neural networks. These conditions are expressed in terms of LMIs, and are dependent on both the discrete and distributed time delays. Therefore, the stability of the neural networks can be checked readily by resorting to the Matlab LMI toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the differentiability of the discrete and distributed time-varying delays, which means that our results generalize and further improve those in the earlier publications. A simulation example is given to show the effectiveness and less conservatism of the obtained conditions.     

Mean square exponential stability of stochastic neural networks with reaction–diffusion terms and delays

In this paper, some sufficient conditions ensuring mean square exponential stability of the equilibrium point of a class of stochastic neural networks with reaction–diffusion terms and time-varying delays are obtained. The conditions involving the effect of diffusion terms reduce the conservatism of the previous results. Finally, we give a numerical example to verify the effectiveness of our results.     

Dynamic analysis of stochastic bidirectional associative memory neural networks with delays

In this paper, stochastic bidirectional associative memory neural networks model with delays is considered. By constructing Lyapunov functionals, and using stochastic analysis method and inequality technique, we give some sufficient criteria ensuring almost sure exponential stability, pth exponential stability and mean value exponential stability. The obtained criteria can be used as theoretic guidance to stabilize neural networks in practical applications when stochastic noise is taken into consideration.     

Robust stability for stochastic Hopfield neural networks with time delays

In this paper, the asymptotic stability analysis problem is considered for a class of uncertain stochastic neural networks with time delays and parameter uncertainties. The delays are time-invariant, and the uncertainties are norm-bounded that enter into all the network parameters. The aim of this paper is to establish easily verifiable conditions under which the delayed neural network is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. By employing a Lyapunov–Krasovskii functional and conducting the stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the stability criteria. The proposed criteria can be checked readily by using some standard numerical packages, and no tuning of parameters is required. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.     

Dynamical behaviors of fuzzy reaction–diffusion periodic cellular neural networks with variable coefficients and delays

When modeling neural networks in a real world, not only diffusion effect and fuzziness cannot be avoided, but also self-inhibitions, interconnection weights, and inputs should vary as time varies. In this paper, we discuss the dynamical behaviors of delayed reaction–diffusion fuzzy cellular neural networks with varying periodic self-inhibitions, interconnection weights as well as inputs. By using Halanay’s delay differential inequality, M$M$-matrix theory and analytic methods, some new sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential stability of the periodic solution, and the exponentially convergent rate index is also estimated. In particular, the traditional assumption on the differentiability of the time-varying delays is no longer needed. The methodology developed in this paper is shown to be simple and effective for the exponential periodicity and stability analysis of neural networks with time-varying delays. Two examples are given to show the usefulness of the obtained results that are less restrictive than recently known criteria.     

随机时滞控制系统的均方BIBO稳定性

本文研究了具有时滞和非线性扰动的随机控制系统的均方有界输入-有界输出(BIBO)稳定.首先,探讨了具有离散时滞和非线性扰动的随机系统的均方BIBO稳定性问题,在此基础上,进一步研究带有离散时滞和分布时滞以及非线性扰动的随机系统的均方BIBO稳定性.通过设计合理的控制器,建立合适的Lyapunov泛函,结合Riccati矩阵方程,得到时滞依赖的均方BIBO稳定性条件.     

Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays

In this paper, the problem of robust exponential stability is investigated for a class of stochastically nonlinear jump systems with mixed time delays. By applying the Lyapunov–Krasovskii functional and stochastic analysis theory as well as matrix inequality technique, some novel sufficient conditions are derived to ensure the exponential stability of the trivial solution in the mean square. Time delays proposed in this paper comprise both time-varying and distributed delays. Moreover, the derivatives of time-varying delays are not necessarily less than 1. The results obtained in this paper extend and improve those given in the literature. Finally, two numerical examples and their simulations are provided to show the effectiveness of the obtained results.