Stability and bifurcation in systems of tri-neurons with multiple time delays

Li, Lei (2006) Stability and bifurcation in systems of tri-neurons with multiple time delays. Masters thesis, Memorial University of Newfoundland.

[img] [English] PDF - Accepted Version
Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.

Download (2172Kb)

Abstract

This Master thesis consists of four chapters, mainly considering the stability and bifurcation in the systems of delay differential equations representing the neural network models containing tri-neurons with time-delayed connections. -- In Chapter 1, some background of neural networks and the motivation of this work are briefly addressed. -- In Chapter 2, we mainly show the stability analysis. By constructing Liapunov functional, we obtain the global stability condition. Then we show the delay-independent and delay-dependent conditions for local stability respectively. -- In Chapter 3, we discuss the bifurcations. By using the center manifold theory and normal form method, we propose the transcritical, pitchfork and Hopf bifurcation analysis. -- In the last chapter, by using the global Hopf bifurcation result and high-dimensional Bendixson's criterion, we show that the local Hopf bifurcation can be extended globally after certain critical values of delay.

Item Type: Thesis (Masters)
URI: http://research.library.mun.ca/id/eprint/10886
Item ID: 10886
Additional Information: Bibliography: leaves 79-85.
Department(s): Science, Faculty of > Mathematics and Statistics
Date: 2006
Date Type: Submission
Library of Congress Subject Heading: Bifurcation theory; Neural networks (Computer science)

Actions (login required)

View Item View Item

Downloads

Downloads per month over the past year

View more statistics