151-0532-00L  Nonlinear Dynamics and Chaos I

SemesterAutumn Semester 2016
LecturersG. Haller, F. Kogelbauer
Periodicityyearly recurring course
Language of instructionEnglish



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, F. Kogelbauer
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
- 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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Courses

NumberTitleHoursLecturers
151-0532-00 VNonlinear Dynamics and Chaos I2 hrs
Wed10-12HG D 7.1 »
G. Haller, F. Kogelbauer
151-0532-00 UNonlinear Dynamics and Chaos I2 hrs
Thu16-18HG D 7.1 »
G. Haller, F. Kogelbauer

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Offered in

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