Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


The student will learn the principles of analysing nonlinear and chaotic dynamical systems using mathematics and diagrammatic methods. Basic understanding of fundamental concepts in chaotic systems such as strange attractors will be obtained.

Credits: 5

Schedule: 12.01.2022 - 11.04.2022

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Riku Linna

Contact information for the course (applies in this implementation):

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English


  • valid for whole curriculum period:

    Flows on the line. Bifurcations. Flows on the plane. Limit cycles. Lorenz equations. One-dimensional maps. Logistic maps. Lyapunov exponents. Fractals.

Assessment Methods and Criteria
  • valid for whole curriculum period:

    Final examination and mathematical/computational exercises.

  • valid for whole curriculum period:

    Lectures: 10 * 1.5 h = 15 h

    Studying the material, completing the assignments, and participating in the exercise sessions: 10 * (1.5+9) h = 105 h

    Preparing for and taking the exam: (16 +4) h = 20 h

    Total: 135 h (= 5 cr * 27 h)


Study Material
  • valid for whole curriculum period:

    S. H. Strogatz, Nonlinear dynamics and chaos. Specific articles may be added.

Substitutes for Courses


Further Information
  • valid for whole curriculum period:

    This course is for Master s students and graduate students.

    Teaching Period:

    2020-2021 Spring III-IV

    2021-2022 Spring III-V

    Course Homepage:

    Registration for Courses: Kurssille ilmoittaudutaan WebOodissa. Katso ilmoittautumisaika WebOodista. Ilmoittautumiseen