Global exponential stability and periodicity of reaction–diffusion recurrent neural networks with distributed delays and Dirichlet boundary conditions

In this paper, global exponential stability and periodicity of a class of reaction–diffusion recurrent neural networks with distributed delays and Dirichlet boundary conditions are studied by constructing suitable Lyapunov functionals and utilizing some inequality techniques. We first prove global exponential convergence to 0 of the difference between any two solutions of the original neural networks, the existence and uniqueness of equilibrium is the direct results of this procedure. This approach is different from the usually used one where the existence, uniqueness of equilibrium and stability are proved in two separate steps. Secondly, we prove periodicity. Sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium and periodic solution are given. These conditions are easy to verify and our results play an important role in the design and application of globally exponentially stable neural circuits and periodic oscillatory neural circuits.     

Exponential stability and periodicity of impulsive cellular neural networks with time delays

This paper is concerned with the stability and periodicity for a class of impulsive neural networks with delays. By means of the Fixed point theory, Lyapunov functional and analysis technique, some sufficient conditions of exponential stability and periodicity are obtained. We can see that impulses do contribution to the stability and periodicity. An example is given to demonstrate the effectiveness of the obtained results.     

Stability and periodicity in delayed cellular neural networks with impulsive effects

In the paper, the global exponential stability and periodicity are investigated for delayed cellular neural networks with impulsive effects. Some sufficient conditions are derived for checking the global exponential stability and the existence of periodic solution for this system based on Halanay inequality, mathematical induction and fixed point theorem. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses, which provides flexibility for the design and analysis of delayed cellular neural networks with impulses.     

Stability and periodicity in high-order neural networks with impulsive effects

In this paper, the global exponential stability and periodicity are investigated for a class generalized high-order neural networks with time delays and impulses; some sufficient conditions are derived for checking the global exponential stability and existence of periodic solutions for this system using the generalized Halanay inequality, mathematical induction and a fixed point theorem. The criteria given are easily verified and possess many adjustable parameters, which provides flexibility for the design and analysis of the system. Finally, an example with numerical simulation is given to show the effectiveness of the proposed method and results.     

Global exponential stability of impulsive discrete-time neural networks with time-varying delays

This paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete-time neural networks with time-varying delays. Firstly, by means of the Lyapunov stability theory, some inequality analysis techniques and a discrete-time Halanay-type inequality technique, sufficient conditions for ensuring global exponential stability of discrete-time neural networks are derived, and the estimated exponential convergence rate is provided as well. The obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete-time neural networks with time-varying delays. Finally, numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria.     

Existence and stability of almost periodic solutions of Hopfield neural networks with continuously distributed delays

In this paper, the global stability and almost periodicity are investigated for Hopfield neural networks with continuously distributed neutral delays. Some sufficient conditions are obtained for the existence and globally exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper are new and they complement the previously known ones. Finally, an example is given to demonstrate the effectiveness of our results.     

Stability of delayed cellular neural networks

Global asymptotic stability and exponential stability of delayed cellular neural networks is considered in this paper. Based on the Lyapunov stability theorem as well as a fact about the elemental inequality, some new sufficient conditions are given for global asymptotic stability and exponential stability of delayed cellular neural networks. The results are less conservative than those established in the earlier references. Three examples are given to illustrate the applicability of these conditions.     

Global exponential stability for nonautonomous cellular neural networks with unbounded delays

Global exponential stability of nonautonomous cellular neural networks with unbounded delays is considered in this paper. By applying Lyapunov functional method, some new sufficient conditions are given for global exponential stability of solutions of the networks. The stability conditions obtained here improve and extend some of the previous conditions. An example is presented to illustrate the applicability of these conditions.     

SCALE-TYPE STABILITY FOR NEURAL NETWORKS WITH UNBOUNDED TIME-VARYING DELAYS

This paper studies scale-type stability for neural networks with unbounded time-varying delays and Lipschitz continuous activation functions. Several sufficient conditions for the global exponential stability and global asymptotic stability of such neural networks on time scales are derived. The new results can extend the existing relevant stability results in the previous literatures to cover some general neural networks.     

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.     

Periodic bi-directional Cohen–Grossberg neural networks with distributed delays

Some sufficient conditions are obtained for the global exponential stability of periodic solutions to periodic bi-directional Cohen–Grossberg neural networks involving distributed delays, by using the Lyapunov functional method and some analytical techniques. These results improve and generalize some previous works, and are helpful for designing a global exponential stable periodic bi-directional Cohen–Grossberg neural networks.     

Novel global robust exponential stability criterion for uncertain BAM neural networks with time-varying delays

In this paper, the global robust exponential stability for a class of delayed BAM neural networks with norm-bounded uncertainty is studied. Some less conservative conditions are presented for the global exponential stability of BAM neural networks with time-varying delays by constructing a new class of Lyapunov functionals combined with free-weighting matrices. This novel approach, based on the linear matrix inequality (LMI) technique, removes some existing restrictions on the system’s parameters, and the derived conditions are easy to verify via the LMI toolbox. Comparisons between our results and previous results admit that our results establish a new set of stability criteria for delayed BAM neural networks.     

STABILITY ANALYSIS OF HOPFIELD NEURAL NETWORKS WITH DELAYS

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New results of global robust exponential stability of neural networks with delays

In this paper, the global robust exponential stability of interval neural networks with delays is investigated. Employing homeomorphism techniques and Lyapunov functions, we establish some sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for delayed neural networks. It is shown that the obtained results improve and generalize the previously published results.     

Cohen-Grossberg神经网络的全局指数稳定性分析

本文研究了CohenGrossberg神经网络模型的指数稳定性.为避免构造Lyapunov函数的困难,我们采用广义相对Dalquist数方法来分析神经网络的稳定性.借助这一方法,我们不但得到了CohenGrossberg神经网络模型平衡解的存在性、唯一性和全局指数稳定性的新的充分条件,而且给出了神经网络的指数衰减估计.所获结论改进了已有文献的相关结果.     

Dynamics of Cohen–Grossberg neural network with variable coefficients and time-varying delays

This paper studies the Cohen–Grossberg neural networks with variable and time-varying delays. By applying Dini derivative and introducing many real parameters, and estimating the upper bound of solutions of the system, a series of new and useful criteria on the uniform boundedness, point dissipativeness and global exponential stability for general Cohen–Grossberg neural networks. And then, some sufficient conditions on the existence and global exponential stability of periodic solutions for periodic Cohen–Grossberg neural networks are established, either. Those results obtained in this paper extend and generalize the corresponding results existing in previous literature. These criteria are important in signal processing and the design of networks.     

Existence and stability of almost periodic solution for Cohen–Grossberg neural networks with variable coefficients

This paper is devoted to the existence and globally exponential stability of almost periodic solution for a class of Cohen–Grossberg neural networks with variable coefficients. By using Banach fixed point theorem and applying inequality technique, we give some sufficient conditions ensuring the existence and globally exponential stability of almost periodic solution. These results have important leading significance in designs and applications of Cohen–Grossberg neural networks. Finally, two examples with their numerical simulations are provided to show the correctness of our analysis.     

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.     

时滞BAM神经网络周期解的存在性和全局指数稳定性

本文利用迭合度理论,通过构造适当的Lyapunov泛函并结合Yang不等式分析技巧,获得了具周期系数的时滞BAM神经网络周期解的存在性和全局指数稳定性的充分条件,这些结果对设计全局指数稳定的BAM神经网络与周期振荡的BAM神经网络具有重要的指导意义.     

DYNAMICS OF NEW CLASS OF HOPFIELD NEURAL NETWORKS WITH TIME-VARYING AND DISTRIBUTED DELAYS

In this paper,we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays.In fact,the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution,which is also its derivative pseudo almost periodic.This results are without resorting to the theory of exponential dichotomy.Furthermore,by employing the suitable Lyapunov function,some delay-independent sufficient conditions are derived for exponential convergence.The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity.Lastly,two examples are given to demonstrate the validity of the proposed theoretical results.