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.

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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.

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