Zengfu Wang

Global Stability of a General Class of Discrete-Time Recurrent Neural Networks

A general class of discrete-time recurrent neural networks (DTRNNs) is formulated and studied in this paper. Several sufficient conditions are obtained to ensure the global stability of DTRNNs with delays based on induction principle (not based on the well-known Liapunov methods). The obtained results have neither assumed the symmetry of the connection matrix, nor boundedness, monotonicity or the differentiability of the activation functions. In addition, discrete-time analogues of a general class of continuous-time recurrent neural networks (CTRNNs) are derived and studied. The convergence characteristics of CTRNNs are preserved by the discrete-time analogues without any restriction imposed on the uniform discretization step size. Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.

ATTRACTABILITY AND LOCATION OF EQUILIBRIUM POINT OF CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS

This paper presents new theoretical results on global exponential stability of cellular neural networks with time-varying delays. The stability conditions depend on external inputs, connection weights and delays of cellular neural networks. Using these results, global exponential stability of cellular neural networks can be derived, and the estimate for location of equilibrium point can also be obtained. Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.

Stability Analysis of Discrete-Time Cellular Neural Networks

Discrete-time cellular neural networks (DTCNNs) are formulated and studied in this paper. Several sufficient conditions are obtained to ensure the global stability of DTCNNs with delays based on comparison methods (not based on the well-known Liapunov methods). Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.

Practical stability criteria for cellular neural networks described by a template

In this paper, we show that the N/spl times/M -dimensional cellular neural networks described by a template can have 2/sup N/spl times/M/ locally exponentially stable equilibrium points located in saturation regions. In particular, we also derive several conditions that the equilibrium point is locally exponentially stable when the equilibrium point locates the designated saturation region. Moreover, these conditions can be checked by direct examination of the template, regardless of the number of cells, and are the improvement and extension of the existing relevant stability results in the literature.

Pattern Recognition Based on Stability of Discrete Time Cellular Neural Networks

In this paper, some sufficient conditions are obtained to guarantee that discrete time cellular neural networks (DTCNNs) can have some stable memory patterns. These conditions can be directly derived from the structure of the neural networks. Moreover, the method of how to estimate of the attracting domain of such stable memory patterns is also described in this paper. In addition, a new design algorithm for DTCNNs is developed based on stability theory (not based on the well-known perceptron training algorithm), and the convergence of the design algorithm can be guaranteed by some stability theorems. Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.

Global Convergence of Steepest Descent for Quadratic Functions

This paper analyzes the effect of momentum on steepest descent training for quadratic performance functions. Some global convergence conditions of the steepest descent algorithm are obtained by directly analyzing the exact momentum equations for quadratic cost functions. Those conditions can be directly derived from the parameters (different from eigenvalues that are used in the existed ones.) of the Hessian matrix. The results presented in this paper are new.

Global exponential stability of delayed Cohen-Grossberg neural networks

In this paper, using a fixed-point theorem and reduction to absurdity, the authors have obtained some sufficient conditions to guarantee that Cohen-Grossberg neural networks with discrete and distributed delays are globally exponentially stable. Since the model is more general and the assumptions relax the previous assumptions in some existing works, the results presented in this paper are the improvement and extension of the existed ones. Finally, the validity and performance of the results are illustrated by two simulation examples.