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.

LEARNING OUTCOMES

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: 13.01.2021 - 12.04.2021

Teacher in charge (valid 01.08.2020-31.07.2022): Riku Linna

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

Contact information for the course (valid 09.12.2020-21.12.2112):

Lecturer:

Riku Linna 

e-mail: riku.linna@aalto.fi

Office: B334 (CS-building)

Assistant:

Pauliina Kärkkäinen

e-mail: pauliina.karkkainen@aalto.fi



CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English

CONTENT, ASSESSMENT AND WORKLOAD

Content
  • Valid 01.08.2020-31.07.2022:

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

  • 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. (S)he will also gain basic understanding on numerically simulating nonlinear systems.

Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    Final examination and mathematical/computational exercises.

  • 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.

    Note: Due to pandemic situation the exam may be replaced by a few small project assignments. This will agree upon as the Cours proceeds.

Workload
  • Valid 01.08.2020-31.07.2022:

    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)

  • 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.


DETAILS

Study Material
  • Valid 01.08.2020-31.07.2022:

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

  • Applies in this implementation:

    Lecture notes covering the required material will be given.

Substitutes for Courses
  • Valid 01.08.2020-31.07.2022:

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

Prerequisites
  • Valid 01.08.2020-31.07.2022:

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

FURTHER INFORMATION

Details on the schedule
  • Applies in this implementation:

    There will be ten lectures and exercise sessions. The first lecture is on Wed Jan 13 and the first exercise session on Thu Jan 21. 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.