Quantitative study of general motion stability

I.Course Introduction (including teaching goals and requirements) within 300 words:

    A novel methodology, trajectory stability-preserving and dimension-reducing (TSPDR), is proposed for analyzing stabilities of nonlinear systems, including bounded stability, unbounded-mode stability, and structural stability. The idea is to first get the time response curves of the system, and then divide the curves into complementary pairs and map them into subspaces of two-degree of freedom by using a suitable linear with stability-preserving transformation, and finally determine the system stability from the projected trajectories. TSPDR combines the universal applicability of numerical integration with quantitative analysis. Based on TSPDR, the complementary-cluster energy-barrier criterion (CCEBC) was employed to deal with the bounded stability of motion of the system. The stability margin can be defined rigorously for the projected trajectories, and the stability margin of the original system is the minimum among all such margins. CCEBC has been implemented as a commercial software package, which is unique with quantitative assessment capability in the world today and has been widely used in power systems in China, Canada, France, and USA. In this study, the coordinate-plane projection (CPP) method is put forward for studying global bifurcation and higher-dimensional chaos. An n-dimensional space X is divided into  and  with n-1 independent patterns. For each pattern, the characteristic equation of X₁ is studied with X₂ as parameters, and the bifurcation sets of X₁ can be analytically expressed as functions of X₂ independent of the changes of X₂(t) in the process. After numerical integration, the actualtrajectories X₁(t) and X₂(t) are shown respectively in the phase plane and the parameter space. Bifurcation occurs whenever X₂(t) intersects the bifurcation sets, thereby the points where the structures of both X₁(t) and X(t) have been changed are identified. Since each bifurcation is rigorously located as well as characterized, the route to chaos can be uniquely symbolized for each trajectory. For illustration, microstructures of Lorenz and Lorenz-like attractors are studied as examples.

II.Teaching Syllabus (including the content of chapters and sections. A sheet can be attached):

See below.（Time is decided  by  lecturer）：

III.Teaching Schedule:

Note: 

1.Above one, two, and three items are used as teaching Syllabus in Chinese and announced on the Chinese website of Graduate School. The four and five items are preserved in Graduate School.

2. Course terms: Spring, Autumn , and Spring-Autumn term. 

3. The teaching languages for courses: Chinese, English or Chinese-English.

4.Applicable range of discipline: public, first-class discipline, second-class discipline, and third-class discipline.

5. Practice includes: experiment, investigation, research report, etc.

6. Teaching methods: lecture, seminar, practice, etc.

7. Examination for degree courses must be in paper.

8. Teaching material websites are those which have already been announced.

9. Brief introduction of chief lecturer should include: personal information (date of birth, gender, degree achieved, professional title), research direction, teaching and research achievements. (within 100-500 words)