6 ECTS credits
150 h study time
Offer 1 with catalog number 4012761ENR for all students in the 2nd semester
at
a (E) Master - advanced level.
- Semester
- 2nd semester
- Enrollment based on exam contract
- Impossible
- Grading method
- Grading (scale from 0 to 20)
- Can retake in second session
- Yes
- Taught in
- English
- Partnership Agreement
- Under interuniversity agreement for degree program
- Faculty
- Faculty of Sciences and Bioengineering Sciences
- Department
- Physics
- Educational team
- Lendert Gelens
Sophie De Buyl
(course titular)
- Activities and contact hours
- 13 contact hours Lecture
13 contact hours Seminar, Exercises or Practicals
13 contact hours Independent or External Form of Study
- Course Content
- General introduction about linear versus nonlinear dynamics.
- Dynamical systems with one variable.
- Bifurcations in one variable systems: saddle-node, cusp, transcritical and imperfect bifurcations.
- Bifurcations on the circle, synchronisation.
- Linear dynamics with two variables: classification of the fixed points (saddle, node, center, degenerate).
- Nonlinear dynamics with two variables: phase space analysis, reversibility, Lyapunov function, theory of the index.
- Limit cycles: relaxation oscillations, singular perturbation.
- Chaos: Lorentz model and analysis.
- One dimensional maps: bifurcations, period doubling and intermittency route to chaos, universality.
- Fractals: self-similarity, fractal dimension.
- Strange attractors: stretching and folding, baker’s map, Henon map.
- Pattern formation.
- Additional info
Course material
Textbook: Nonlinear Dynamics and Chaos With Applications to Physics, Biology, Chemistry, and Engineering, Steven H. Strogatz (Ebook ISBN: 9780813349114)
Additional info
A copy of the lecture slides will be provided
Useful skills: linear algebra (matrix manipulation, eigenvectors and eigenvalues), solving ordinary differential equations, basic python skills.
- Learning Outcomes
-
Algemene competenties
The overall objective of this course is to be able to analyze dynamical systems using geometrical methods on the phase space. This includes carrying out linear stability, bifurcation and phase plane analyses. We will first focus on one and two dimensional systems. Chaotic phenomena in physical systems will be described with two classical examples: the Lorentz strange attractor and the logistic map. Solving problems and reading literature related to the course material is also foreseen.
- Grading
-
The final grade is composed based on the following categories:
Oral Exam determines 60% of the final mark.
PRAC Presentation determines 40% of the final mark.
Within the Oral Exam category, the following assignments need to be completed:
- Written exam
with a relative weight of 60
which comprises 60% of the final mark.
This is a mid-term test.
Note: oral exam with a written preparation (theory and exercises)
Within the PRAC Presentation category, the following assignments need to be completed:
- Presentation
with a relative weight of 40
which comprises 40% of the final mark.
Note: presentation of group work (during the classes)
- Additional info regarding evaluation
- oral exam with a written preparation (theory and exercises) for 60% of the final grade.
- presentation of a group projet (during one of the classes) for 40% of the final grade.
- Allowed unsatisfactory mark
- The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.
Academic context
This offer is part of the following study plans:
Master of Physics and Astronomy: Minor Research
Master of Physics and Astronomy: Minor Economy and Business
Master of Physics and Astronomy: Minor Education
Master of Teaching in Science and Technology: fysica (120 ECTS, Etterbeek) (only offered in Dutch)