On the stability analysis of delayed neural networks systems

In this paper, the problems of stability of delayed neural networks are investigated, including the stability of discrete and distributed delayed neural networks. Under the generalization of dropping the Lipschitzian hypotheses for output functions, some stability criteria are obtained by using the Liapunov functional method. We do not assume the symmetry of the connection matrix and we establish that the system admits a unique equilibrium point in which the output functions do not satisfy the Lipschitz conditions and do not require them to be differential or strictly monotonously increasing. These criteria can be used to analyze the dynamics of biological neural systems or to design globally stable artificial neural networks.

Convergence in discrete-time neural networks with specific performance

We analyze convergence in discrete-time neural networks with specific performance such as decay rate and trajectory bounds in terms of componentwise absolute (exponential) stability. Simple necessary and sufficient stability and positive invariance conditions are presented, which allow us to design a convergent network with prescribed performance. Our approach is based on a decomposition of competitive-cooperative connectivity or inhibitory-excitatory interaction that abounds in neural networks, without assuming symmetry of the connection matrices. The key idea is that through the decomposition, we can always relate a competitive-cooperative network with a cooperative dynamical system. The latter possesses significant order-preserving properties that are basic to our analysis. The explicit division of connection weights into inhibitory and excitatory types offers a higher potential for relating formal neural network models to neurophysiology.

Neural networks in analog hardware--design and implementation issues

This paper presents a brief review of some analog hardware implementations of neural networks. Several criteria for the classification of general neural networks implementations are discussed and a taxonomy induced by these criteria is presented. The paper also discusses some characteristics of analog implementations as well as some trade-offs and issues identified in the work reviewed. Parameters such as precision, chip area, power consumption, speed and noise susceptibility are discussed in the context of neural implementations. A unified review of various "VLSI friendly" algorithms is also presented. The paper concludes with some conclusions drawn from the analysis of the implementations presented.

Periodic solutions and exponential stability in delayed cellular neural networks

Some simple sufficient conditions are given ensuring global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov functionals and some analysis techniques. These conditions are easy to check in terms of system parameters and have important leading significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. In addition, two examples are given to illustrate the theory.

Global stability analysis in delayed cellular neural networks

In this paper, the author analyzes further problems of global stability for a class of cellular neural networks with delays by means of the Lyapunov functional method, inequalities a(2)+b(2)> or =2ab and a(3)+b(3)+c(3)> or =3abc (a,b,c > or =0) analysis technique, some stability criteria are obtained under more general conditions. These criteria can be applied to design globally stable networks and thus have important significance in both theory and applications.

Analysis and optimal design of continuous neural networks with applications to associative memory

The asymptotic stability of a continuous neural network is analyzed for associative memory. An optimal design method is proposed which ensures the highest associative memory speed and guarantees the storage of each desired memory with attractivity. The network asymptotic stability is analyzed by means of a new energy function, and four theorems are obtained. By comparing these theorems with existing ones, it can be shown that in some cases they are consistent, while in others they are not equivalent but complementary to each other. Further study results in two more generalized conclusions, of which the existing conclusions are special cases. The network optimal design method is proposed in terms of an optimal associative memory theorem. Two application examples are presented to demonstrate the defeffectiveness of the optimal design method, which can be used to design the network for many applications.

Optical implementation of cellular neural networks based on bias and joint correlation

A new bias method for the optical implementation of cellular neural networks is proposed to reduce electronic precalculation and increase processing speed. A multiple-object joint transform correlator is then used to realize the summation of multiple correlations resulting from the bias method. Compared with other optical systems for cellular neural networks, the proposed method offers the advantages of higher processing speed, easy implementation, and robustness. Computer simulations of the optical cellular neural networks for edge detection and corner and horizontal line extraction are also presented.

A neural-network method for the nonlinear servomechanism problem

The solution of the nonlinear servomechanism problem relies on the solvability of a set of mixed nonlinear partial differential and algebraic equations known as the regulator equations. Due to the nonlinear nature, it is difficult to obtain the exact solution of the regulator equations. This paper proposes to solve the regulator equations based on a class of recurrent neural network, which has the features of a cellular neural network. This research not only represents a novel application of the neural networks to numerical mathematics, but also leads to an effective approach to approximately solving the nonlinear servomechanism problem. The resulting design method is illustrated by application to the well-known ball and beam system.

On the analysis of neural networks with asymmetric connection weights or noninvertible transfer functions

This paper extends the energy function to the analysis of the stability of neural networks with asymmetric interconnections and noninvertible transfer functions. Based on the new energy function, stability theorems and convergent criteria are derived which improve the available results in the literature. A simpler proof of a previous result for complete stability is given. Theorems on complete stability of neural networks with noninvertible output functions are presented.

Stability analysis of delayed cellular neural networks

In this paper, the problems of stability in a class of delayed cellular neural networks (DCNN) are studied; some new stability criteria are obtained by using the Lyapunov functional method and some analysis techniques. These criteria can be used to design globally stable networks and thus have important significance in both theory and application.

A survey of partially connected neural networks

Almost all artificial neural networks are by default fully connected, which often implies a high redundancy and complexity. Little research has been devoted to the study of partially connected neural networks, despite its potential advantages like reduced training and recall time, improved generalization capabilities, reduced hardware requirements, as well as being a step closer to biological reality. This publication presents an extensive survey of the various kinds of partially connected neural networks, clustered into a clear framework, followed by a detailed comparative discussion.

Optimal solutions for cellular neural networks by paralleled hardware annealing

An engineering annealing method for optimal solutions of cellular neural networks is presented. Cellular neural networks are very promising in solving many scientific problems in image processing, pattern recognition, and optimization by the use of stored program with predetermined templates. Hardware annealing, which is a paralleled version of mean-field annealing in analog networks, is a highly efficient method of finding optimal solutions of cellular neural networks. It does not require any stochastic procedure and henceforth can be very fast. The generalized energy function of the network is first increased by reducing the voltage gain of each neuron. Then, the hardware annealing searches for the globally minimum energy state by continuously increasing the gain of neurons. The process of global optimization by the proposed annealing can be described by the eigenvalue problems in the time-varying dynamic system. In typical nonoptimization problems, it also provides enough stimulation to frozen neurons caused by ill-conditioned initial states.