Date of Graduation
Master of Science in Mathematics
Nonlinear differential equations are often effective tools in modeling some important phenomena in nature. However, most of the nonlinear ordinary differential equation cannot be solved by analytical methods. A more effective way is to explore the prop- erties of critical point and the trajectory around it. In this study, I will focus on sys- tems of autonomous differential equations, linear as well as nonlinear. I will not only focus on the stability of equilibria but also the orbital stability of nonlinear differential equations. I will introduce various approaches to the study of equilibrium points of the system in terms of their stability properties, illustrated by some applied models. The theory and applications show the great power of mathematical analysis.
stability, nonlinear differential equations, critical points, linearization, Liapunov function, limit circle.
Ordinary Differential Equations and Applied Dynamics
© Jiaxiao Wei
Wei, Jiaxiao, "Stability Theory of Nonlinear Differential Equations" (2021). MSU Graduate Theses. 3708.