Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).
Overview
- Swedish nameDynamiska system
- CodeTIF155
- Credits7.5 Credits
- OwnerMPCAS
- Education cycleSecond-cycle
- Main field of studyEngineering Physics
- DepartmentPHYSICS
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language English
- Application code 11115
- Block schedule
- Open for exchange studentsYes
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0107 Examination 7.5 c Grading: TH | 7.5 c |
|
In programmes
- MPCAS - COMPLEX ADAPTIVE SYSTEMS, MSC PROGR, Year 1 (compulsory)
- MPENM - ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
- MPENM - ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)
- MPSYS - SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Year 1 (elective)
Examiner
- Kristian Gustafsson
- Senior Lecturer, Institution of physics at Gothenburg University
Eligibility
General entry requirements for Master's level (second cycle)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Specific entry requirements
English 6 (or by other approved means with the equivalent proficiency level)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Course specific prerequisites
Sufficient knowledge of Mathematics (analysis in one real variable, linear algebra), basic programming skills.
Aim
The aim of the course is to give an understanding of theoretical concepts and practical aspects arising in the description of nonlinear dynamical systems: how is chaos measured and characterised? How can one detect deterministic chaos in an experimental time series? How can one control and predict chaotic systems? Applications in physics, biology, and economics are described.
Learning outcomes (after completion of the course the student should be able to)
After successfully completing this course the students shall be able tounderstand and explain key concepts in regular dynamical systems;
perform linear stability analysis, and understand its limitations;
analyze qualitative changes in the system as control parameters change (bifurcations);
understand and explain the key concepts used in describing deterministic chaos in non-linear systems;
efficiently simulate dynamical systems on a computer;
numerically compute Lyapunov exponents and fractal dimensions;
efficiently search for periodic orbits and determine their stabilities;
recognize and analyse chaotic dynamics in initially unfamiliar contexts;
communicate results and conclusions in a clear and logical fashion.
Content
Regular dynamics:
Continuous flows.
Fixed points and stability analysis.
Characterisation of linear and non-linear flows.
Bifurcations och structural stability.
Index theory.
Periodic motion, limit cycles and relaxation oscillators.
Chaotic dynamics:
Lyapunov exponents.
Strange attractors.
Fractal dimension, fractals in physical systems.
Transitions to chaos.
Chaos and regular dynamics in Hamiltonian systems.
Organisation
Lectures, set of homework problems, examples classes, and written exam.
Literature
Lecture notes will be made available.
Course book: Nonlinear Dynamics and Chaos, by Stephen H. Strogatz.
Recommended additional material:
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by Guckenheimer and Holmes
ChaosBook by Cvitanovic
Examination including compulsory elements
The final grade is based on four sets of homework assignments (50%) and a written examination (50%).
The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.