Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2006 Elsevier Ltd.This Letter is concerned with the global asymptotic stability analysis problem for a class of uncertain stochastic Hopfield neural networks with discrete and distributed time-delays. By utilizing a Lyapunov–Krasovskii functional, using the well-known S-procedure and conducting stochastic analysis, we show that the addressed neural networks are robustly, globally, asymptotically stable if a convex optimization problem is feasible. Then, the stability criteria are derived in terms of linear matrix inequalities (LMIs), which can be effectively solved by some standard numerical packages. The main results are also extended to the multiple time-delay case. Two numerical examples are given to demonstrate the usefulness of the proposed global stability condition.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms

In this paper, a new global exponential stability criterion is obtained for a general multidimensional delay difference equation using induction arguments. In the cases that the difference equation is periodic, we prove the existence of a periodic solution by constructing a type of Poincar\'e map. The results are used to obtain stability criteria for a general discrete-time neural network model with a delay in the leakage terms. As particular cases, we obtain new stability criteria for neural network models recently studied in the literature, in particular for low-order and high-order Hopfield and Bidirectional Associative Memory(BAM).Comment: 20 pages, 3 figure

Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays

The ordinary Takagi-Sugeno (TS) fuzzy models have provided an approach to represent complex nonlinear systems to a set of linear sub-models by using fuzzy sets and fuzzy reasoning. In this paper, stochastic fuzzy Hopfield neural networks with time-varying delays (SFVDHNNs) are studied. The model of SFVDHNN is first establisbed as a modified TS fuzzy model in which the consequent parts are composed of a set of stochastic Hopfield neural networks with time-varying delays. Secondly, the global exponential stability in the mean square for SFVDHNN is studied by using the Lyapunov-Krasovskii approach. Stability criterion is derived in terms of linear matrix inequalities (LMIs), which can be effectively solved by some standard numerical packages. © 2005 IEEE.published_or_final_versio

Modeling and control of complex dynamic systems: Applied mathematical aspects

The concept of complex dynamic systems arises in many varieties, including the areas of energy generation, storage and distribution, ecosystems, gene regulation and health delivery, safety and security systems, telecommunications, transportation networks, and the rapidly emerging research topics seeking to understand and analyse. Such systems are often concurrent and distributed, because they have to react to various kinds of events, signals, and conditions. They may be characterized by a system with uncertainties, time delays, stochastic perturbations, hybrid dynamics, distributed dynamics, chaotic dynamics, and a large number of algebraic loops. This special issue provides a platform for researchers to report their recent results on various mathematical methods and techniques for modelling and control of complex dynamic systems and identifying critical issues and challenges for future investigation in this field. This special issue amazingly attracted one-hundred-and eighteen submissions, and twenty-eight of them are selected through a rigorous review procedure

General criteria for asymptotic and exponential stabilities of neural network models with unbounded delays

For a family of differential equations with infinite delay, we give sufficient conditions for the global asymptotic, and global exponential stability of an equilibrium point. This family includes most of the delayed models of neural networks of Cohen-Grossberg type, with both bounded and unbounded distributed delay, for which general asymptotic and exponential stability criteria are derived. As illustrations, the results are applied to several concrete models studied in the literature, and a comparison of results is given.Fundação para a Ciência e a Tecnologia (FCT) - 2009-ISFL-1-209Universidade do Minho. Centro de Matemática (CMAT

A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.In this Letter, the analysis problem for the existence and stability of periodic solutions is investigated for a class of general discrete-time recurrent neural networks with time-varying delays. For the neural networks under study, a generalized activation function is considered, and the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By employing the latest free-weighting matrix method, an appropriate Lyapunov–Krasovskii functional is constructed and several sufficient conditions are established to ensure the existence, uniqueness, and globally exponential stability of the periodic solution for the addressed neural network. The conditions are dependent on both the lower bound and upper bound of the time-varying time delays. Furthermore, the conditions are expressed in terms of the linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Two simulation examples are given to show the effectiveness and less conservatism of the proposed criteria.This work was supported in part by the National Natural Science Foundation of China under Grant 50608072, an International Joint Project sponsored by the Royal Society of the UK and the National Natural Science Foundation of China, and the Alexander von Humboldt Foundation of Germany