Скачать или смотреть Lecture 25A | (Interlude) Local stability of ODE periodic orbits

♠課程說明
Course Description:
Delay differential equations are a type of differential equation where the rate of change of a system at a particular time depends not only on its current state but also on its state at previous times. This time delay can represent time lags in physical, biological, or other dynamical systems where the effect of an action is not instantaneous. We will study delay differential equations from the perspective of infinite-dimensional dynamical systems, exploring the impact of time delays on nonlinear phenomena. Specifically, we will first cover the existence, uniqueness, and stability of solutions, followed by important applications such as time-delayed feedback control and global bifurcation.


♠課程目標
Course Objectives:
1. Become familiar with studying delay differential equations from the perspective of
dynamical systems.
2. Master the theories of existence, uniqueness, and stability of solutions.
3. Introduce important applications of delay differential equations, such as time-delayed
feedback control and global bifurcation.


♠參考用書
References (not textbooks, sorted alphabetically):
1. O. Diekmann, S. A. van Gils, S. M. Verduyn Lunel, H.-O. Walther: Delay Equations, Springer,
1995.
2. R. D. Driver: Ordinary and Delay Differential Equations, Springer, 1977.
3. T. Erneux: Applied Delay Differential Equations, Springer, 2009.
4. J. K. Hale: Theory of Functional Differential Equations Springer, 1977.
5. J. K. Hale, S. M. Verduyn Lunel: Introduction to Functional Differential Equations, Springer,
1993.
6. H. Smith: An Introduction to Delay Differential Equations with Applications to the
Life Sciences, Springer, 2011.


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