Year
2025
Season
Fall
Paper Type
Master's Thesis
College
College of Arts and Sciences
Degree Name
Master of Science in Mathematical Sciences (MS)
Department
Mathematics & Statistics
NACO controlled Corporate Body
University of North Florida. Department of Mathematics and Statistics
Committee Chairperson
Dr. Mei-Qin Zhan
Second Advisor
Dr. Kening Wang
Third Advisor
Dr. Mohammad Rahman
Department Chair
Dr. Richard F. Patterson
College Dean
Kaveri Subrahmanyam
Abstract
This thesis presents a rigorous framework for the study of bifurcation phenomena in nonlinear differential equations. Semigroup theory and index theory are introduced to examine qualitative changes in the solution structures of the nonlinear dynamic system as the parameters vary. The theoretical framework is then applied to several nonlinear differential equations from biology and physics.
Suggested Citation
Yesmin, Asrafi, "Bifurcation and index theory with applications to nonlinear differential equations" (2025). UNF Graduate Theses and Dissertations. 1370.
https://digitalcommons.unf.edu/etd/1370