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151-0532-00L 4 Credits BSC , MSC D-ITET , D-MAVT , D-MATH , D-PHYS , D-ERDW , D-INFK
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Nonlinear Dynamics and Chaos I

Lecturers & Examiners: Prof. Dr. George Haller
VVZ CR 3.8

Last Updated: 2026-06-01 11:31:05

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.

Learning Materials (Links)

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
  • Tue 16:15-18:00 (HG D 7.2)
  • Wed 10:15-12:00 (HG D 7.1)
4 h weekly

Offered In