Credits: 5

Schedule: 09.01.2019 - 11.04.2019

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


Riku Linna


Office: B334 (CS-building)


Tarmo Nurmi


Teaching Period (valid 01.08.2018-31.07.2020): 

III (Spring)

Content (valid 01.08.2018-31.07.2020): 

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

Details on the course content (applies in this implementation): 

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.

Assessment Methods and Criteria (valid 01.08.2018-31.07.2020): 

Final examination and mathematical/computational exercises.

Elaboration of the evaluation criteria and methods, and acquainting students with the evaluation (applies in this implementation): 

Doing and returning exercises is optional but highly recommended for those wanting to learn. No exercise points are required to take the exam but you can compensate for maximum of 20 % of exam points with completed exercises. There  is a threshold of 10 % of assignment points; total points exceeding this threshold will (after appropriate scaling) contribute to compensation points in the exam.  

Details on calculating the workload (applies in this implementation): 

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)


The division of studying hours, of course, varies depending on to which extent the assignments are completed.

Study Material (valid 01.08.2018-31.07.2020): 

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

Details on the course materials (applies in this implementation): 

Lecture notes covering the required material will be given.

Substitutes for Courses (valid 01.08.2018-31.07.2020): 

Replaces the former course BECS-114.7151 Nonlinear Dynamics and Chaos and CS-E5750 Nonlinear Dynamics and Chaos.

Prerequisites (valid 01.08.2018-31.07.2020): 

The student should be familiar with differential equations, linear algebra, and programming.

Grading Scale (valid 01.08.2018-31.07.2020): 


Further Information (valid 01.08.2018-31.07.2020): 

This course is for Master’s students and graduate students.

Details on the schedule (applies in this implementation): 

There will be ten lectures and exercise sessions. The first lecture is on Wed Jan 9 and the first exercise session on Thu Jan 17. Each assignment will be given by the time of a weekly lecture and students wishing to have their assignment graded are to return their solutions by the next lecture. The solutions will be shown and discussed on the exercise session on the following Thursday. 


Registration and further information