Periodic bidirectional associative memory neural networks with distributed delays

Some sufficient conditions are obtained for the existence and global exponential stability of a periodic solution to the general bidirectional associative memory (BAM) neural networks with distributed delays by using the continuation theorem of Mawhin's coincidence degree theory and the Lyapunov functional method and the Young's inequality technique. These results are helpful for designing a globally exponentially stable and periodic oscillatory BAM neural network, and the conditions can be easily verified and be applied in practice. An example is also given to illustrate our results.     

Global exponential stability for interval general bidirectional associative memory (BAM) neural networks with proportional delays

This paper is concerned with interval general bidirectional associative memory (BAM) neural networks with proportional delays. Using appropriate nonlinear variable transformations, the interval general BAM neural networks with proportional delays can be equivalently transformed into the interval general BAM neural networks with constant delays. The sufficient condition for the existence and uniqueness of equilibrium point of the model is established by applying Brouwer's fixed point theorem. By constructing suitable delay differential inequalities, some sufficient conditions for the global exponential stability of the model are obtained. Two examples are given to illustrate the effectiveness of the obtained results. This paper ends with a brief conclusion. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

具分布时滞神经网络周期解的指数稳定性

本文利用一些分析技巧,获得了具分布时滞的双向联想记忆（BAM）神经网络模型周期解的指数稳定性的结论。     

Exponential periodic attractor of discrete-time BAM neural networks with transmission delays

In this paper, we investigate discrete-time bidirectional associative memory (BAM) neural networks with periodic coefficients and transmission delays. By using matrix measure, spectral theory, and contraction theory, some sufficient conditions are attained for the existence of a unique exponential periodic attractor. Finally, computer simulations illustrate the dynamic behavior of the unique exponential periodic attractor. Moreover, the unique exponential periodic attractor is also given precisely. The numerical simulation is performed to show our results.     

Periodic oscillation for BAM neural networks with impulses

In this paper, a class of neural networks called bidirectional associative memory (BAM) networks with impulses is discussed. Some sufficient conditions are established for the existence and global exponential stability of a unique periodic solution and the exponentially convergent rate is estimated. The sufficient conditions are easy to be verified and when the impulsive jumps are absent, the results reduce to those of the non-impulsive systems. The approaches are based on employing inequality analysis, matrix theory and its spectral theory.     

连续型BAM神经网络的指数稳定性

首先将连续型双向联想记忆神经网络转化成一个特殊的Hopfield网络模型.在此基础上,对连续BAM神经网络的指数稳定性进行了新的分析,证明了神经网络连接权矩阵在给定的约束条件下有唯一平衡点.所做的分析可以用于设计全局指数稳定的神经网络.     

A new sufficient condition for global robust stability of bidirectional associative memory neural networks with multiple time delays

This paper presents an easily verifiable delay independent sufficient condition for the global robust asymptotic stability of the equilibrium point for bidirectional associative memory (BAM) neural networks with time delays by employing a class of Lyapunov functionals. The obtained results are applicable to all bounded continuous non-monotonic neuron activation functions. Some numerical examples are given to compare our results with the previous robust stability results derived in the literature.     

Some criteria for robust stability of Cohen–Grossberg neural networks with delays

This paper considers the problem of robust stability of Cohen–Grossberg neural networks with time-varying delays. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, some sufficient conditions are derived to ensure the global robust convergence of the equilibrium point. The proposed LMI conditions can be checked easily by recently developed algorithms solving LMIs. Comparisons between our results and previous results admits our results establish a new set of stability criteria for delayed Cohen–Grossberg neural networks. Numerical examples are given to illustrate the effectiveness of our results.     

Global exponential stability for BAM neural networks with time-varying delays in the leakage terms

In this paper, we first investigate the existence of a unique equilibrium to general bidirectional associative memory neural networks with time-varying delays in the leakage terms by the fixed point theorem. Then, by constructing a Lyapunov functional, we establish some sufficient conditions on the global exponential stability of the equilibrium for such neural networks, which substantially extend and improve the main results of Gopalsamy [K. Gopalsamy, Leakage delays in BAM, J. Math. Anal. Appl. 325 (2007) 1117–1132].     

Exponential stability of positive neural networks in bidirectional associative memory model with delays

This paper is concerned with the problem of exponential stability of positive neural networks in bidirectional associative memory (BAM) model with multiple time‐varying delays and nonlinear self‐excitation rates. On the basis of a systematic approach involving extended comparison techniques via differential inequalities, we first prove the positivity of state trajectories initializing from a positive cone called the admissible set of initial conditions. In combination with the use of Brouwer's fixed point theorem and M‐matrix theory, we then derive conditions for the existence and global exponential stability of a unique positive equilibrium of the model. An extension to the case of BAM neural networks with proportional delays is also presented. The effectiveness of the obtained results is illustrated by a numerical example with simulations.     

p/q-Type criteria for stability analysis in higher order Cohen-Grossberg-type bidirectional associative memory neural networks with time delays

In this paper, we investigate the higher order Cohen-Grossberg-type bidirectional associative memory (BAM) neural networks with time delays. By using Lyapunov-Kravsovskii functional and homeomorphism theory, some new sufficient conditions are established for the existence and global exponential stability of a unique equilibrium without strict conditions imposed on self regulation functions. Finally, an example and its simulations are presented to illustrate the global exponential stability of the equilibrium.     

Dynamics of high-order BAM neural networks with and without impulses

The main aim of this paper is to study the existence and global exponential stability of periodic solution for high-order bidirectional associative memory (BAM) neural networks with and without impulses. Easily verifiable sufficient conditions are established. The method is based on coincidence degree theory as well as a priori estimates and Lyapunov functional. It is shown that the convergence characteristics of periodic solution for the impulsive system are preserved by the corresponding nonimpulsive system with some restriction imposed on the impulse effect. Numerical simulation results are given to support the theoretical predictions.     

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 analysis of bidirectional associative memory neural networks with time-varying delays

In this paper, global exponential stability is studied for a class of high-order bidirectional associative memory (BAM) neural networks with time-varying delays. An approach combining the Lyapunov functional with the Linear Matrix Inequality (LMI) is taken to study the problems. Several sufficient conditions are presented for ensuring the system to be globally exponentially stable. Three typical examples are presented to show the application of the criteria obtained in this paper.     

Exponential periodic attractor of impulsive BAM networks with finite distributed delays

In this paper, we investigate a class of impulsive bidirectional associative memory (BAM) networks with both periodic coefficients and finite distributed delays. New criteria are established for the existence of an exponential periodic attractor, which generalize and improve the previously known results. Our criteria are less restrictive and can be applied to impulsive or non-impulsive BAM networks with a broad range of activation functions without differentiability and strict monotonicity. Moreover, our results are given in terms of system parameters and finite delay kernels of impulsive BAM networks by employing inequality technique, M-matrix and spectral theory. Finally, an example is given to show the feasibility and effectiveness of our results.     

具有时滞的双向联想记忆(BAM)的神经网络的全局动力学行为

在没有假定关联函数的光滑性,单调性和有界性的条件下,应用Liapunov泛函方法和矩阵代数技术,得到具有常数传输时滞的双向联想记忆(BAM)的神经网络模型平衡点存在性和全局指数稳定性的一些新的充分条件,这些条件可以由网络参数,连接矩阵和关联函数的Lipschitz常数所表示的M矩阵来刻化．这些结果不仅是简单和实用的,而且相对于已有文献的结果具有较少的限制和更易于验证．     

Robust passivity analysis of fuzzy Cohen-Grossberg BAM neural networks with time-varying delays

This paper is concerned with the problem of passivity analysis for a class of Cohen-Grossberg fuzzy bidirectional associative memory (BAM) neural networks with time varying delay. By employing the delay fractioning technique and linear matrix inequality optimization approach, delay dependent passivity criteria are established that guarantees the passivity of fuzzy Cohen-Grossberg BAM neural networks with uncertainties. The passivity condition is expressed in terms of LMIs, which can be easily solved by various convex optimization algorithms. Finally, a numerical example is given to illustrate the effectiveness of the proposed result.     

Exponential stability for stochastic jumping BAM neural networks with time-varying and distributed delays

In this paper we study the stability for a class of stochastic jumping bidirectional associative memory (BAM) neural networks with time-varying and distributed delays. To the best of our knowledge, this class of stochastic jumping BAM neural networks with time-varying and distributed delays has never been investigated in the literature. The main aim of this paper tries to fill the gap. By using the stochastic stability theory, the properties of a Brownian motion, the generalized Ito’s formula and linear matrix inequalities technique, some novel sufficient conditions are obtained to guarantee the stochastically exponential stability of the trivial solution or zero solution. In particular, the activation functions considered in this paper are fairly general since they may depend on Markovian jump parameters and they are more general than those usual Lipschitz conditions. Also, the derivative of time delays is not necessarily zero or small than 1. In summary, the results obtained in this paper extend and improve those not only with/without noise disturbances, but also with/without Markovian jump parameters. Finally, two interesting examples are provided to illustrate the theoretical results.     

Exponential stability for stochastic reaction-diffusion BAM neural networks with time-varying and distributed delays

In this paper we study the stability for a class of stochastic bidirectional associative memory (BAM) neural networks with reaction-diffusion and mixed delays. The mixed delays considered in this paper are time-varying and distributed delays. Based on a new Lyapunov-Krasovskii functional and the Poincaré inequality as well as stochastic analysis theory, a set of novel sufficient conditions are obtained to guarantee the stochastically exponential stability of the trivial solution or zero solution. The obtained results show that the reaction-diffusion term does contribute to the exponentially stabilization of the considered system. Moreover, two numerical examples are given to show the effectiveness of the theoretical results.