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

Nonlinear Dynamics and Chaos I

Lecturers & Examiners: Prof. Dr. George Haller

VVZ CR 3.8

Last Updated: 2026-06-03 00:07:42

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

Written and typed lecture notes are available in Moodle, as well as recorded lecture videos from an earlier year.

General Information

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

Examination

Type: end-of-semester examination
Mode: written 120 minutes
Aids: No typed or handwritten materials allowed; a formula sheet will be provided. No further materials or electronic devices are allowed.

Course Components

Type	Title	Time & Place	Hours
lecture with exercise	Nonlinear Dynamics and Chaos I	No time listed	4 h weekly

Offered In

Mechanical Engineering Bachelor
- Bachelor Studies (Programme Regulations 2022)
  - Focus Specialization
    - Design, Mechanics and Manufacturing (Focus Coordinator: Prof. Dennis Kochmann To achieve the required 20 credit points for the Focus Specialization Design, Mechanics and Manufacturing, all of the courses listed can be selected. If required, one course from another focus specialization or from the electives of the ME Bachelor program can be selected. For recommended courses and further information, please visit the MAVT website for Focus Specialization ( ).)
Mechanical Engineering Master
- Core Courses (The Core Courses in the Master’s program Mechanical Engineering listed below are indicative and include courses designed by the Department at the Master's level. With the approval of the tutor, students may also select Master's-level courses offered by other departments at ETH. These courses will be marked as non-regular in the LAG, but their categorization as Core Courses is possible if included in the approved LAG.)
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
- 01 - Courses of specializations
  - 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. Semester / Research Projects are not allowed in this category. A minimum of 40 credits must be obtained from specialisation courses during the Master's Programme.)
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
Space Systems Master
- Deep Track Courses (At least 20 credits must be completed within the deep track courses. Surplus credit points can be counted towards the electives.)
  - Aerospace Engineering
    - Elective Courses Aerospace Engineering (These subjects can only be credited as electives.)