Coupled nonlinear differential equations. Phase space, trajectories. Iterative maps. Stability analysis of singular points. Limit cycles, strange attractors. Poincaré-Bendixson theorem. Bifurcations. Chaos. Lyapunov exponents. Feigenbaum renormalization. Fractals, fractal dimensions. Lorenz equations, logistic map, Hénon map, Rössler system. Applications to Physics, Biology, Chemistry, Engineering: Lasers. Superconducting Josephson junctions. Population dynamics. Chemical kinetics. Electronic oscillators. Nonlinear mechanical systems.
FSI3090 Complex Systems 7.5 credits
Information per course offering
Course offerings are missing for current or upcoming semesters.
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus FSI3090 (Spring 2019–)Headings with content from the Course syllabus FSI3090 (Spring 2019–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
Intended learning outcomes
After completed course, the PhD student should be able to:
- be familiar with analytical and numerical methods for the analysis of coupled nonlinear differential equations.
- interpret and characterize different solution types.
- know, and be able to develop, applications to physics, biology, chemistry, engineering, and other areas.
Literature and preparations
Specific prerequisites
Basic course in differential equations.
Literature
Steven H. Strogatz: Nonlinear Dynamics and Chaos (Westview Press, 2000, ISBN 0-7382-0453-6).
Examination and completion
Grading scale
P, F
Examination
- INL1 - Assignments, 5.0 credits, grading scale: P, F
- TEN1 - Oral exam, 2.5 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
If the course is discontinued, students may request to be examined during the following two academic years.
Other requirements for final grade
Home assignments and an oral exam.
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.
Offered by
Education cycle
Third cycle