Abstract: In this paper, by employing a new Lyapunov functional
and an elementary inequality analysis technique, some sufficient
conditions are derived to ensure the existence and uniqueness of
periodic oscillatory solution for fuzzy bi-directional memory (BAM)
neural networks with time-varying delays, and all other solutions of
the fuzzy BAM neural networks converge the uniqueness periodic
solution. These criteria are presented in terms of system parameters
and have important leading significance in the design and applications
of neural networks. Moreover an example is given to illustrate the
effectiveness and feasible of results obtained.
Abstract: In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of discrete Hopfield neural networks with delays. Some new stability criteria for system are derived by using the Lyapunov functional method and the linear matrix inequality approach, for estimating the upper bound of Lyapunov functional derivative.
Abstract: The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-dependent population equations with Poisson random measures. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.
Abstract: The problem of exponential stability and periodicity for a class of cellular neural networks (DCNNs) with time-varying delays is investigated. By dividing the network state variables into subgroups according to the characters of the neural networks, some sufficient conditions for exponential stability and periodicity are derived via the methods of variation parameters and inequality techniques. These conditions are represented by some blocks of the interconnection matrices. Compared with some previous methods, the method used in this paper does not resort to any Lyapunov function, and the results derived in this paper improve and generalize some earlier criteria established in the literature cited therein. Two examples are discussed to illustrate the main results.