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Nonlinear Dynamics and Chaos I
Last Updated: 2026-02-05 15:35:19
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.
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- MSC
- Frequency
- Yearly recurring
Examination
- Type
- end-of-semester examination
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture |
Nonlinear Dynamics and Chaos I
The lecturers will communicate the exact lesson times of ONLINE courses.
|
|
2 h weekly |
| exercise |
Nonlinear Dynamics and Chaos I
The lecturers will communicate the exact lesson times of ONLINE courses.
|
|
2 h weekly |
Offered In
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Mechanics, Materials, Structures (The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.)
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Robotics, Systems and Control (The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.)
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Electives (In the ‘electives’ subcategory, at least two course units must be successfully completed.)
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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.)
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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.)
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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.)
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Recommended Subjects (These courses are recommended, but you are free to choose courses from any other special field. Please consult your tutor.)
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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.))
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