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151-0532-00L 4 Credits BSC , MSC D-ITET , D-MAVT , D-MATH , D-PHYS , D-INFK

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Nonlinear Dynamics and Chaos I

Lecturers & Examiners: Prof. Dr. George Haller

VVZ CR 3.8

Last Updated: 2026-02-05 16:15:06

Abstract

Basic facts about nonlinear systems; stability and near-equilibrium dynamics; bifurcations; dynamical systems on the plane; non-autonomous dynamical systems; chaotic dynamics.

Objective

This 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

Resources

Lecture Notes

The class lecture notes will be posted electronically after each lecture. Students should not rely on these but prepare their own notes during the lecture.

General Information

Language: English
Levels: BSC , MSC
Frequency: Yearly recurring

Examination

Type: end-of-semester examination
Mode: written 120 minutes
Aids: Written aids Students can use handwritten or typed class lecture notes during the written exam. No further materials or electronic devices are allowed.

Course Components

Type	Title	Time & Place	Hours
lecture	Nonlinear Dynamics and Chaos I	Wed 10:15-12:00 (HG D 7.1)	2 h weekly
exercise	Nonlinear Dynamics and Chaos I	Tue 16:15-18:00 (HG D 7.2)	2 h weekly

Offered In

Mechanical Engineering Bachelor
- Bachelor Studies (Programme Regulations 2010)
  - Focus Specialization
    - Design, Mechanics and Manufacturing (Focus Coordinator: Prof. Dennis Kochmann In order to achieve the required 20 credit points for the Focus Specialization Design, Mechanics and Manufacturing you are free to choose any of the courses offered within the focus. If you wish to take one of the Master level courses, you must get approval from the lecturer. One course in addition to those listed can be requested, on approval by the Focus Coordinator.)
Mechanical Engineering Master
- Core Courses
  - Mechanics, Materials, Structures (The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.)
  - Robotics, Systems and Control (The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.)
Computational Science and Engineering Master
- Fields of Specialization
  - Fluid Dynamics (One of the course units 151-0103-00L Fluid Dynamics II 151-0109-00L Turbulent Flows is compulsory. Students able to follow courses in German are advised to choose 151-0103-00L Fluid Dynamics II.)
  - Systems and Control
Mathematics Master
- Electives (Direction Applied Mathematics MSc Only) (Electives from applied mathematics and further application-oriented fields that are only eligible for credits for the Master's degree in Applied Mathematics.)
Micro- and Nanosystems Master
- Core Courses
  - Elective Core Courses
Electrical Engineering and Information Technology Master
- Master Studies (Programme Regulations 2018)
  - Track: Systems and Control (The core courses and specialisation courses below are a selection for students who wish to specialise in the area of "Systems and Control", see . The individual study plan is subject to the tutor's approval.)
    - Specialisation Courses (These specialisation courses are particularly recommended for the area of "Systems and Control", but you are free to choose courses from any other field in agreement with your tutor. A minimum of 40 credits must be obtained from specialisation courses during the Master's Programme.)
- Master Studies (Programme Regulations 2008)
  - Major Courses (A total of 42 CP must be achieved during the Master Programme. The individual study plan is subject to the tutor's approval.)
    - Systems and Control
      - Recommended Subjects (These courses are recommended, but you are free to choose courses from any other special field. Please consult your tutor.)
Physics Master
- Electives
  - General Electives (Students may choose General Electives from the entire course programme of ETH Zurich - with the following restrictions: courses that belong to the first or second year of a Bachelor curriculum at ETH Zurich as well as courses from GESS "Science in Perspective" are not eligible here. The following courses are explicitly recommended to physics students by their lecturers. (Courses in this list may be assigned to the category "General Electives" directly in myStudies. For the category assignment of other eligible courses keep the choice "no category" and take contact with the Study Administration ( ) after having received the credits.))
Robotics, Systems and Control Master
- Core Courses