Dynamics of some neural network models

Wang, Lin (2003) Dynamics of some neural network models. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

This Ph.D. dissertation consists of four chapters and mainly deals with the dynamics of several neural network models described by delay differential equations, difference equations and stochastic differential equations. -- In Chapter 1, some background of neural networks and the motivations of this work are briefly addressed. -- In Chapter 2, Liapunov functional method and the theory of monotone dynamical systems are employed to obtain some delay independent and delay dependent stability results for the general continuous-time Cohen-Grossberg neural networks with distributed delays. Detailed local stability and bifurcation analysis are also given in this chapter for the bidirectional associative memory (BAM) neural networks with and without self-connections. -- Chapter 3 is devoted to the study of discrete-time neural networks with delays. Specifically, we first derive some global stability results for the discrete-time neural networks with variable delays and then investigate the capacity of the discrete-time BAM neural networks by giving the number of all possible stable periodic solutions. -- The stochastic neural networks are studied in Chapter 4, in which some criteria for the almost sure exponential stability, mean square exponential stability are established for stochastic Cohen-Grossberg neural networks with and without delays.

Item Type: Thesis (Doctoral (PhD))
URI: http://research.library.mun.ca/id/eprint/9889
Item ID: 9889
Additional Information: Bibliography: leaves 141-154.
Department(s): Science, Faculty of > Mathematics and Statistics
Date: 2003
Date Type: Submission
Library of Congress Subject Heading: Neural networks (Computer science)--Mathematical models.

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