Graduation Semester and Year

2009

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Jianzhong Su

Abstract

In this work, we use analysis and numerical simulations to study the change of collective behaviorof two synaptically coupled square bursting systems, the effect of noise inan elliptic bursting system and foreign body reactions.For the square bursters we study its synchronization process as the strength ofcoupling increases. The two cells present chaotic bursting behaviorwhen there is no coupling. As the strength increases and past a certain value,the behavior of two cells, which are uncoupled, becomes synchronized regular burstingmotions. For the elliptic bursting phenomenon we study the distribution of the noise and its effects in the dynamics and the reliability of the firing pattern. Finally, we study foreign body reactions to implants. A computational model is constructed to investigate the time dynamics of the reaction kinetics of the major elements involved in the fibrosis formation process.

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

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