Researches On Dynamical Properties Of Recurrent Neural Networks With Delays

The study of the dynamical properties of recurrent neural networks has been an important topic in the neural network field since the Hopfield neural network model was proposed in 1982. For the most applications of neural networks (e.g., optimization, associative memory, signal processing, image processing, and pattern recognition), the basic qualitative properties of the network model are the global stability of the equilibrium point. For this reason, the dynamical properties of two types of recurrent neural networks with delays (i.e., Hopfield neural networks and Cohen-Grossberg neural networks) are investigated detailed in this dissertation. The main content concerns the analysis for the globally asymptotic stability of Hopfield neural networks and Cohen-Grossberg neural networks, which is independent of the delays; the analysis for the global stability of Cohen-Grossberg neural networks, which is dependent of the delays; the investigation on the robust stability of two types of recurrent neural networks with delays, when the uncertainties are norm-bounded and satisfy a certain match condition. The main contributions of this dissertation are summarized as follows:1. This dissertation outlines the development of neural networks and analyzes the effect of delays on the stability of neural networks. The basic theories used in the chapters are introduced, including the conception of stability, several common Lyapunov stability theorems, and the lemmas of the linear matrix inequality approach.2. The dynamic properties of a class of Hopfield neural networks with time delays are investigated. Without assuming the symmetric properties of interconnecting structure, the stability of a class of the Hopfield neural network model with time delays and asymmetric interconnecting structure is considered. The criterion of the globally asymptotic stability of equilibrium point is given via the method of constructing a suitable Lyapunov functional and sector condition. By the definition and properties of matrix norm, a corollary expressed by matrix norm is obtained. In the process of design and implementation of Hopfield neural networks, the conditions are very applicable. The simulation samples have proved the effectiveness of the results.3. The robust stability of a class of Hopfield neural networks with delays and parameter perturbations is analyzed. When the uncertainties are norm-bounded and satisfy a certain match condition, the sufficient conditions for the global robust...