151-0532-00L  Nonlinear Dynamics and Chaos I

SemesterSpring Semester 2016
LecturersG. Haller
Periodicityyearly recurring course
CourseDoes not take place this semester.
Language of instructionEnglish
CommentThis course will take place in the Autumn Semester from 2016 onwards.



Courses

NumberTitleHoursLecturers
151-0532-00 VNonlinear Dynamics and Chaos I
Does not take place this semester.
2 hrsG. Haller
151-0532-00 UNonlinear Dynamics and Chaos I
Does not take place this semester.
1 hrsG. Haller

Catalogue data

AbstractBasic facts about nonlinear systems; stability and near-equilibrium dynamics; bifurcations; dynamical systems on the plane; non-autonomous dynamical systems; chaotic dynamics.
ObjectiveThis course is intended for Masters and Ph.D. students in engineering sciences, physics and applied mathematics who are interested in the behavior of nonlinear dynamical systems. It offers an introduction to the qualitative study of nonlinear physical phenomena modeled by differential equations or discrete maps. We discuss applications in classical mechanics, electrical engineering, fluid mechanics, and biology. A more advanced Part II of this class is offered every other year.
Content(1) Basic facts about nonlinear systems: Existence, uniqueness, and dependence on initial data.

(2) Near equilibrium dynamics: Linear and Lyapunov stability

(3) Bifurcations of equilibria: Center manifolds, normal forms, and elementary bifurcations

(4) Nonlinear dynamical systems on the plane: Phase plane techniques, limit sets, and limit cycles.

(5) Time-dependent dynamical systems: Floquet theory, Poincare maps, averaging methods, resonance
Lecture notesThe class lecture notes will be posted electronically after each lecture. Students should not rely on these but prepare their own notes during the lecture.
Prerequisites / Notice- Prerequisites: Analysis, linear algebra and a basic course in differential equations.

- Exam: two-hour written exam in English.

- Homework: A homework assignment will be due roughly every other week. Hints to solutions will be posted after the homework due dates.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits4 credits
ExaminersG. Haller
Typeend-of-semester examination
Language of examinationEnglish
RepetitionThe performance assessment is only offered at the end after the course unit. Repetition only possible after re-enrolling.
Additional information on mode of examination- Written 120 minutes
- Grade policy: 25% of the final grade is based on the homework assignment (one randomly selected exercise from each homework will be graded). The remaining 75% of the final grade is based on the exam.
- Written aids: Students can use the class lecture notes and a calculator during the written exam. No further material is allowed.

Learning materials

 
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Offered in

ProgrammeSectionType
Electrical Engineering and Information Technology MasterRecommended SubjectsWInformation
Mechanical Engineering BachelorDesign, Mechanics and MaterialsWInformation
Mechanical Engineering MasterMechanics, Materials, StructuresWInformation
Mechanical Engineering MasterRobotics, Systems and ControlWInformation
Micro- and Nanosystems MasterElective Core CoursesWInformation
Physics MasterGeneral ElectivesWInformation
Robotics, Systems and Control MasterCore CoursesWInformation