Physics of Complex Systems: Dynamics and Chaos

3 EC

Semester 1, period 1

5354PCSD3Y

Owner Master Physics and Astronomy (joint degree)
Coordinator Edan Lerner
Part of Master Physics and Astronomy, track Advanced Matter and Energy Physics, Master Physics and Astronomy, track Theoretical Physics, Master Computational Science (Joint Degree), Master Physics and Astronomy (joint degree), track Biophysics and Biophotonics, Master Physics and Astronomy (joint degree), track General Physics and Astronomy,

Course manual 2025/2026

Course content

This course will focus on (nonlinear) dynamical systems, and will cover the following subjects:

  1. Low-dimensional dynamical systems with regular attractors: fixed points, limit cycles and bifurcations
  2. Linear stability analysis
  3. Low-dimensional dynamical systems with irregular attractors: chaos and fractals

Students are expected to solve exercises that include a computational component.

Study materials

Literature

  • Steven H Strogatz, "Nonlinear Dynamics and Chaos" (main textbook)

  • Lecture notes

Software

  • MATLAB, Python, Mathematica or computational language of choice

Objectives

  • Students will learn to analyze low dimensional dynamical systems, construct their phase portraits, classify their fixed points and bifurcations
  • Understand how and under what conditions chaos emerges in low-dimensional nonlinear dynamic systems, and how it is quantified
  • Learn to use numerical integration in order to investigate the dynamics of nonlinear systems.
  • Learn to calculate the fractal dimension of various systems/objects

Teaching methods

  • Lecture
  • Self-study
  • Homework assignments

Learning activities

Activity

Hours

Hoorcollege

14

Tentamen

3

Werkcollege

14

Self study

53

Total

84

(3 EC x 28 uur)

Attendance

  • Some course components require compulsory attendance. If compulsory attendance applies, this will be indicated in the Course Catalogue which can be consulted via the UvA-website. The rationale for and implementation of this compulsory attendance may vary per course and, if applicable, is included in the Course Manual.

    • Assessment

    Item and weight Details

    Final grade

    0.65 (100%)

    Tentamen

    The grade is comprised of the homework exercises (35%) and the final exam (65%)

    Assignments

    2-3 compulsory, graded exercises will be given. The exercises will include numerical components, and must be carried out individually. 

    Fraud and plagiarism

    The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

    Course structure

    Week Topic (tentative)
    1 Introduction to dynamical systems, 1D flows
    2 Bifurcations
    3 2D flows
    4 Limit cycles and bifurcations in 2D
    5 Logistic map I
    6 Logistic map II
    7 Lorenz Equations
    8 Final exam

    Contact information

    Coordinator

    • Edan Lerner

    Staff

    • Tommaso Pettinari [t.pettinari@uva.nl] will TA this course