Dynamical Behavior Of A Class Of High-order Hopfield Neural Networks With Time Delays

Hopfield neural network is a kind of nonlinear information processing system,which has been widely used in image processing, pattern recognition, signalprocessing and control theory. Therefore, it is becoming more and more important toinvestigate the dynamical behavior of Hopfield neural network, such as exponentialstability, invariant and attracting sets. Higher-order Hopfield neural network is morefunctional than the lower one. More and more people becoming interested in the studyof high-order neural network as time going on.The dynamical behavior of a class of high-order Hopfield neural networks withtime delays were discussed in this paper．In the first chapter, the general knowledge of neural networks is introduced, andthe preliminary knowledge which is used in the thesis is given.In the second chapter, by using the theory of topological degree and Lyapunovfunctional methods, the global exponential stability of a class of multiple high-orderneural networks with distributed time delays is discussed. The existence uniquenessand global asymptotic stability of equilibrium point are investigated. The result isillustrated by an example.In the third chapter, by using the theory of nonnegative matrices and differentialinequalities technique the invariant and attracting sets of a class of multiple high-orderneural networks with distributed time delays is discussed. The sufficient condition ofthe invariant and attracting sets of this class of competitive neural networks given.The result is illustrated by an example.In the fourth chapter, the global stable in the mean square of high-order neuralnetwork is discussed by using Ito ’s formula and LMI theorem. The result is illustratedby an example.