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We have analyzed the stability of interactional genetic regulatory networks with reaction-diffusion terms under Dirichlet boundary conditions in this article. Corresponding to interaction between unstable genetic regulatory networks and stable genetic regulatory networks, the model is given, and a stability criterion is proposed through construction of appropriate Lyapunov-Krasovskii functions and linear matrix inequalities (LMI). By means of a numerical simulation, we have proved the effectiveness and correctness of the theorem, and we analyzed the factors that influence the stability for interactional genetic regulatory networks. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we obtain some sufficient conditions for determining the asymptotic stability of discrete-time non-autonomous delayed Hopfield neural networks by utilizing the Lyapunov functional method. An example is given to show the validity of the results. [Copyright &y& Elsevier]

Abstract: By constructing suitable Lyapunov functionals and combining with matrix inequality technique, a new sufficient condition is presented for the global asymptotic stability of delayed neural networks. The condition contains and improves some of the previous results in the earlier references. [Copyright &y& Elsevier]

Abstract: In this paper, by utilizing the Lyapunov functional method and combining with the linear matrix inequality approach, we analyze the global asymptotic stability of delayed Hopfield neural networks (HNNs). A new sufficient condition ensuring the global stability of the unique equilibrium point of delayed HNNs is obtained, which is dependent on the size of delays. This condition is less restrictive and conservative than that given in the earlier references. In addition, an example is also provided to illustrate the applicability of the result. [Copyright &y& Elsevier]

A new sufficient condition has been presented ensuring the global exponential stability of cellular neural networks with time-varying delays by using an approach based on delay differential inequality combining with Young inequality. The results established here extend those earlier given in the literature. Compared with the method of Lyapunov functionals as in most previous studies, our method is simpler and more effective for stability analysis. [Copyright &y& Elsevier]

Some new sufficient conditions for the global exponential stability and estimations of bound on the rate of exponential convergence of the neural networks with time-varying delays are obtained by means of an approach based on delay differential inequality. The method, which does not make use of any Lyapunov functionals, is simple and valid for the stability analysis of neural networks with time-varying delays. Some previously established results in the literature are shown to be special cases of the presented results. [Copyright &y& Elsevier]

A model of Hopfield neural networks (HNN) with continuously distributed delays is considered. A sufficient condition which guarantees global exponential stability (GES) of an equilibrium point is given based on the method of variation parameter and inequality technique. Compared with the previous methods, our method does not resorting to any Lyapunov functionals. [Copyright &y& Elsevier]

In this study, we propose two techniques for clustering genetic regulatory networks with mixed delays. Laws for identifying coupling parameters are designed, and the Lyapunov theorem and Lipschitz condition are employed to achieve the desired stability and to identify the coupling parameters. Using our proposed methods, the value of a cluster or the sum of clusters can approach the expected values. Numerical examples verify the feasibility and effectiveness of this method. [ABSTRACT FROM AUTHOR]