數學

層級：	課程資料
媒體：	影音

延時微分方程

2024-09-05-2040-12-31

國立清華大學數學系戴佳原

關鍵字：延時微分方程

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.

教學進度
Course schedule

Week	Date	Content
1	09/05	Introduction to DDEs
2	09/12	Are DDEs finite- or infinite-dimensional? Viewpoint of dynamical systems
3	09/19	Existence, uniqueness, and continuation; Eventually compact semiflows
4	09/26	(Interlude) Local stability of ODE equilibria; Linear autonomous FDEs
5	10/03	# Typhoon Holiday
6	10/10	# Holiday
7	10/17	Characteristic equations; Infinitely many eigenvalues of linear discrete DDEs
8	10/24	Stability region; Spectral effect of small delays
9	10/31	# Typhoon Holiday
10	11/07	Spectral effect of large delays; Example: Neutral differential difference equations
11	11/14	Variation-of-constant formula for linear discrete DDEs
12	11/21	(Interlude) Local stability of ODE periodic orbits
13	11/28	Pyragas feedback control stabilization; Example: Subcritical Stuart-Landau oscillators;
		Limitation of Pyragas control
14	12/05	DDEs of negative feedback type; Global attractors; Zero number

評分標準
Grading Criteria

♠	Homework 70 %, final exam 30 %

注意事項
Important Notice

♠	Plagiarism in assignments and cheating in exams are strictly prohibited in this course.
	If substantial evidence confirms plagiarism in assignments or cheating in exams,the semester grade will be recorded as zero.

生成式人工智慧倫理聲明
Generative AI Ethics Statement

♠	This course allows students to use generative AI in their learning process, but be aware that
	generative AI still contains many errors and may affect the understanding of fundamental core knowledge. When using generative AI, students must adhere to the ethical guidelines provided in the course.

前往課程 View Course
https://ocw.nthu.edu.tw/ocw/index.php?page=course&cid=345&

數學

延時微分方程

相關課程