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.     

Existence and exponential stability of almost periodic solutions for neutral‐type BAM neural networks with distributed leakage delays

This paper is concerned with a class of neutral‐type BAM neural networks with distributed leakage delays. By applying the exponential dichotomy of linear differential equations, Lyapunov functional method and contraction mapping principle, we establish some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such BAM neural networks. An example is given to illustrate the effectiveness of the theoretical findings. The results obtained in this article are completely new and complement the previously known studies. Copyright © 2016 John Wiley & Sons, Ltd.     

NEW CRITERIA OF EXPONENTIAL STABILITY FOR BAM NEURAL NETWORKS WITH DELAYS

In this Letter,a novel Lyapunov functional is constructed to investigate the exponential stability of the BAM neural networks.New sufficient conditions of the uniqueness and global exponential stability for the equilibrium of BAM neural networks with delays are obtained.The results improve those existing ones.     

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.     

Exponential stability and periodic solution for fuzzy BAM Neural networks with time varying delays

In this paper, a class of fuzzy BAM neural networks with time varying delays is discussed. By using the properties of M-matrix, Linear Matrix Inequality（LMI） approach and general Lyapunov-Krasovskii functional, some new sufficient conditions are derived to ensure the existence of periodic solutions and the global exponential stability of the fuzzy BAM neural networks with time varying delays. These results have important significance in the design of global exponential stable BAM networks with delays. Moreover, an example is given to illustrate that the conditions of the results in the paper are feasible.     

变时滞BAM神经网络的全局指数稳定性

研究一类变时滞BAM神经网络平衡点的全局指数稳定性问题.在不要求激励函数全局Lipschitz条件下,通过构造合适的Lyapunov泛函,并结合Young不等式,得到了BAM神经网络模型在一定条件下全局指数稳定的一些充分条件,推广和改进了前人的相关结论,为综合设计指数稳定的时滞BAM神经网络提供了依据.     

Exponential stability for markovian jumping stochastic BAM neural networks with mode‐dependent probabilistic time‐varying delays and impulse control

In this article, an exponential stability analysis of Markovian jumping stochastic bidirectional associative memory (BAM) neural networks with mode‐dependent probabilistic time‐varying delays and impulsive control is investigated. By establishment of a stochastic variable with Bernoulli distribution, the information of probabilistic time‐varying delay is considered and transformed into one with deterministic time‐varying delay and stochastic parameters. By fully taking the inherent characteristic of such kind of stochastic BAM neural networks into account, a novel Lyapunov‐Krasovskii functional is constructed with as many as possible positive definite matrices which depends on the system mode and a triple‐integral term is introduced for deriving the delay‐dependent stability conditions. Furthermore, mode‐dependent mean square exponential stability criteria are derived by constructing a new Lyapunov‐Krasovskii functional with modes in the integral terms and using some stochastic analysis techniques. The criteria are formulated in terms of a set of linear matrix inequalities, which can be checked efficiently by use of some standard numerical packages. Finally, numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 20: 39–65, 2015     

EXISTENCE AND STABILITY OF PERIODIC SOLUTIONS OF DELAYED BAM NEURAL NETWORKS WITH PERIODIC COEFFICIENTS

In this paper, we study the BAM neural networks with variable coefficients and delays. By using the Banach fixed point theorem and constructing suitable Lyapunov function, we obtain some sufficient conditions ensuring the existence, uniqueness and global stability of periodic solution. These results are helpful to design global exponential stable BAM networks and periodic oscillatory BAM networks.     

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.     

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.     

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.     

Existence and global exponential stability of almost periodic solutions for BAM neural networks with distributed leakage delays on time scales

In this paper, we deal with a class of BAM neural networks with distributed leakage delays on time scales. Some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such class of BAM neural networks are obtained by applying the exponential dichotomy of linear differential equations, Lapunov functional method and contraction mapping principle. An example is given to illustrate the effectiveness of the theoretical predictions. The obtained results in this paper are completely new and complement the previously known publications.     

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.     

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。     

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.     

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.     

具有时滞的一般型脉冲神经网络的指数稳定性

讨论具有时滞的一般性脉冲神经网络的稳定性.在不假定激励函数有界或可导的前提下,利用非光滑分析和Lyapunov泛函,得到了这类神经网络系统平衡点的存在唯一性和全局指数稳定性判别准则.作为特例,得到了Hopfield神经网络,时滞细胞神经网络,双向联想记忆神经网络的平衡点的存在唯一性和全局指数稳定性判定定理.     

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].     

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.     

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.