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This paper concentrates on the problem of global exponential periodicity and stability of memristive neural networks with variable delays. By constructing the appropriate Lyapunov functionals and utilizing some inequality techniques, new algebraic criteria are proposed to guarantee the existence and global exponential stability of periodic solution of the considered system. In addition, the proposed theoretical results not only expand and complement the earlier publications, but also are easy to be checked with the parameters of system itself. A numerical example is given to demonstrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this paper, several simple and new conditions are presented to ensure existence, uniqueness and global exponential robust stability of the equilibrium point of neural networks with delays by using contraction mapping principle, homeomorphism property and Lyapunov method. The conditions given in this paper are easy to verify and apply, and the obtained results improve and extend to those in the literature. In addition, two examples are given to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of exponential stability for recurrent neural networks with multiple time-varying delays and reaction-diffusion terms. The activation functions are supposed to be bounded and globally Lipschitz continuous. By means of Lyapunov functionals, sufficient conditions are derived, which guarantee global exponential stability of the delayed neural network. Finally, a numerical example is given to show the correctness of our analysis. [ABSTRACT FROM AUTHOR]

In the present paper the question of global asymptotic stability of a class of impulsive delayed cellular neural networks with dynamical thresholds is considered. The main results are obtained by means of piecewise continuous Lyapunov functions. The Razumikhin technique is used. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new robust stability analysis method for uncertain cellular neural networks with time-varying delay. The proposed stability criterion is based on the Lyapunov function with sector bounded nonlinear function. The sufficient condition for the stability is derived in terms of LMI (linear matrix inequality). Numerical examples show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: The discrete delayed Hopfield neural networks is an extension of the discrete Hopfield neural networks. In this paper, the convergence of discrete delayed Hopfield neural networks is mainly studied, and some results on the convergence are obtained by using Lyapunov function. Several new sufficient conditions for the delayed networks converging towards a limit cycle with period at most 2 are proved in parallel updating mode. Also, some conditions for the delayed networks converging towards a limit cycle with 2-period are investigated in parallel updating mode. All results established in this paper extend the previous results on the convergence of both the discrete Hopfield neural networks, and the discrete delayed Hopfield neural networks in parallel updating mode. [Copyright &y& Elsevier]

Abstract: Employing the matrix measure approach and Lyapunov function, the author studies the global exponential stability of delayed neural networks with impulses in this paper. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point for such delayed neural networks with impulses. Finally, three examples are given to show the effectiveness of the results obtained here. [Copyright &y& Elsevier]

The article discusses the issue of designing a dynamic ship positioning system making use of the adaptive vectorial backstepping method and RBF type artificial neural networks. In the article, the backstepping controller is used to determine control laws and neural network weight adaptation laws. The artificial neural network is applied at each time instant to approximate nonlinear functions containing parametric uncertainties. The proposed control system does not require precise knowledge of the model of ship dynamics and external disturbances, it also eliminates the problem of analytical determination of the regression matrix when designing the control law with the aid of the adaptive backstepping procedure. [ABSTRACT FROM AUTHOR]

Without assuming boundedness and differentiability of the activation functions and any symmetry of interconnections, we employ Lyapunov functions to establish some sufficient conditions ensuring existence, uniqueness, global asymptotic stability, and even global exponential stability of equilibria for the Cohen-Grossberg neural networks with and without delays. Our results are not only presented in terms of system parameters and can be easily verified and also less restrictive than previously known criteria and can be applied to neural networks, including Hopfield neural networks, bidirectional association memory neural networks, and cellular neural networks. [ABSTRACT FROM AUTHOR]