Delay-dependent exponential stability for impulsive Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms

In this paper, a class of impulsive Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion is formulated and investigated. By employing delay differential inequality and the linear matrix inequality (LMI) optimization approach, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive Cohen–Grossberg neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of Cohen–Grossberg neural networks. An example is given to show the effectiveness of the results obtained here.     

Stability in impulsive Cohen-Grossberg-type BAM neural networks with distributed delays

In this paper, a class of impulsive Cohen-Grossberg-type bi-directional associative memory (BAM) neural networks with distributed delays is investigated. By establishing an integro-differential inequality with impulsive initial conditions and employing the homeomorphism theory, the M-matrix theory and inequality technique, some new general sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive Cohen-Grossberg-type BAM neural networks with distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the system parameters and impulsive disturbed intension. An example is given to show the effectiveness of the results obtained here.     

A new criterion to global exponential stability for impulsive neural networks with continuously distributed delays

This paper considers the global exponential stability and exponential convergence rate of impulsive neural networks with continuously distributed delays in which the state variables on the impulses are related to the unbounded distributed delays. By establishing a new impulsive delay differential inequality, a new criterion concerning global exponential stability for these networks is derived, and the estimated exponential convergence rate is also obtained. The result extends and improves on earlier publications. In addition, two numerical examples are given to illustrate the applicability of the result. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamics of fuzzy impulsive bidirectional associative memory neural networks with time-varying delays

Complex nonlinear systems can be represented to a set of linear sub-models by using fuzzy sets and fuzzy reasoning via ordinary Takagi-Sugeno (TS) fuzzy models. In this paper, the exponential stability of TS fuzzy bidirectional associative memory (BAM) neural networks with impulsive effect and time-varying delays is investigated. The model of fuzzy impulsive BAM neural networks with time-varying delays established as a modified TS fuzzy model is new in which the consequent parts are composed of a set of impulsive BAM neural networks with time-varying delays. Further the exponential stability for fuzzy impulsive BAM neural networks is presented by utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) technique without tuning any parameters. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.     

Global exponential stability of BAM neural networks with time-varying delays: The discrete-time case

This paper deals with the problem of stability analysis for a class of discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient conditions is proposed for the global exponential stability of discrete-time BAM neural networks. The proposed LMI based results can be easily checked by LMI control toolbox. Moreover, an example is also provided to demonstrate the effectiveness of the proposed method.     

Exponential convergence estimates for neural networks with discrete and distributed delays

In this paper, the problems of determining the global exponential stability and estimating the exponential convergence rate are investigated for a class of neural networks with mixed discrete and distributed time-varying delays. By employing a new Lyapunov–Krasovskii functional, a linear matrix inequality (LMI) approach is exploited to establish sufficient easy-to-test conditions for the neural networks to be globally exponentially stable, which can be readily solved by using the numerically efficient Matlab LMI toolbox. Three numerical examples are provided to demonstrate the effectiveness of the proposed results.     

Exponential stability of impulsive high-order cellular neural networks with time-varying delays

The paper considers the problems of global exponential stability for impulsive high-order neural networks with time-varying delays. By employing the Hardy inequality and the Lyapunov functional method, we present some new criteria ensuring exponential stability. The activation functions are not assumed to be differentiable or strictly increasing, and no assumption on the symmetry of the connection matrices is necessary. These criteria are important in signal processing and the design of networks. Moreover, we also extend the previously known results. One illustrative example is also given in the end of this paper to show the effectiveness of our results.     

An analysis on existence and global exponential stability of periodic solutions for BAM neural networks with time-varying delays

In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using analytic methods, inequality technique and M-matrix theory, several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of periodic solution are derived. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. Some existing results are improved and extended. The obtained results are less restrictive than previously known criteria, and the hypothesis for the boundedness and monotonicity on the activation functions and the differentiability on the time-varying delays are removed. An example is given to show the effectiveness of the obtained results.     

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.     

变时滞Hopfield神经网络的全局吸引性和全局指数稳定性

对一类具时滞的Hopfeild型神经网络模型,在非线性神经元激励函数只要求满足Lipschitz连续的条件下,利用推广的Halanay时延微分析不等式、Dini导数以及泛函微分析技术,给出了这类模型的平衡点全局指数稳定性和全局吸引性的充分条件,这些条件易于检验,且改进和推广了前人的结论.此外,此文给出了研究神经网络模型的全局吸引性的微分不等式比较方法.     

Exponential stability of reaction-diffusion high-order Markovian jump Hopfield neural networks with time-varying delays

This paper studies the problems of global exponential stability of reaction-diffusion high-order Markovian jump Hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential stability in the mean square for the reaction-diffusion high-order neural networks are established, which are easily verifiable and have a wider adaptive. An example is also discussed to illustrate our results.     

Global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays

In this paper, by means of constructing the extended impulsive delayed Halanay inequality and by Lyapunov functional methods, we analyze the global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays. Some new sufficient conditions ensuring exponential stability of the unique equilibrium point of impulsive Hopfield neural networks with time delays are obtained. Those conditions are more feasible than that given in the earlier references to some extent. Some numerical examples are also discussed in this work to illustrate the advantage of the results we obtained.     

Stability analysis of impulsive parabolic complex networks

In the present paper, two kinds of impulsive parabolic complex networks (IPCNs) are considered. In the first one, all nodes have the same time-varying delay. In the second one, different nodes have different time-varying delays. Using the Lyapunov functional method combined with the inequality techniques, some global exponential stability criteria are derived for the IPCNs. Furthermore, several robust global exponential stability conditions are proposed to take uncertainties in the parameters of the IPCNs into account. Finally, numerical simulations are presented to illustrate the effectiveness of the results obtained here.     

Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays

This paper is concerned with the existence and global exponential stability of periodic solution for a class of impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays. Some sufficient conditions ensuring the existence and global exponential stability of periodic solution are derived by constructing a suitable Lyapunov function and a new differential inequality. The proposed method can also be applied to study the impulsive Cohen-Grossberg-type BAM neural networks with finite distributed delays. The results in this paper extend and improve the earlier publications. Finally, two examples with numerical simulations are given to demonstrate the obtained results.     

A graph-theoretic approach to exponential stability of BAM neural networks with delays and reaction-diffusion

This paper deals with the problem of global exponential stability for bidirectional associate memory (BAM) neural networks with time-varying delays and reaction-diffusion terms. By using some inequality techniques, graph theory as well as Lyapunov stability theory, a systematic method of constructing a global Lyapunov function for BAM neural networks with time-varying delays and reaction-diffusion terms is provided. Furthermore, two different kinds of sufficient principles are derived to guarantee the exponential stability of BAM neural networks. Finally, a numerical example is carried out to demonstrate the effectiveness and applicability of the theoretical results.     

Impulsive delay differential inequality and stability of neural networks

In this article, a generalized model of neural networks involving time-varying delays and impulses is considered. By establishing the delay differential inequality with impulsive initial conditions and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, some new sufficient conditions for global exponential stability of impulsive delay model are obtained. The results extend and improve the earlier publications. An example is given to illustrate the theory.     

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.     

Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms

In this paper, the global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms is considered. By establishing an integro-differential inequality with impulsive initial condition and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, several new sufficient conditions are obtained to ensure the global exponential stability of the equilibrium point for fuzzy cellular neural networks with delays and reaction-diffusion terms. These results extend and improve the earlier publications. Two examples are given to illustrate the efficiency of the obtained results.     

Global exponential stability of impulsive Cohen–Grossberg neural network with time-varying delays

In this paper, the impulsive Cohen–Grossberg neural network model with time-varying delays is considered. Applying the idea of vector Lyapunov function, M-matrix theory and inequality technique, several new sufficient conditions are obtained to ensure global exponential stability of equilibrium point for impulsive Cohen–Grossberg neural network with time-varying delays. These results generalize a few previous known results and remove some restrictions on the neural network. An example is given to show the effectiveness of the obtained results. It is believed that these results are significant and useful for the design and applications of the Cohen–Grossberg neural network.