FSG3045 Non-linear Oscillations and Dynamical Systems 7.5 credits

Flows and mappings, state space formulations, geometrical methods, limit sets, bifurcations, Poincaré mappings, chaos.

After the course the student should be able to: 

• Explain how ordinary differential equations (ODE) and iterated maps give rise to dynamical system. 
• Be able to define the state space, its limit sets and attractors. 
• Explain how the state space dimension limits the possible dynamics. 
• Sketch the limit set and starting from this characterize the main features in the flow of a dynamical system given by ODEs in the plane. 
• Recognize and describe the result of a simulation using the concept of Poincare mapping. 
• Know about and be able to calculate the fractal dimension in a few simple cases. 
• Know about the concept of chaos in dynamical systems and state some properties of a chaotic dynamical system.

Linear algebra, multivariable calculus, ordinary differential equations, basic mechanics, numerical methods.

Strogatz, S. H. 1994. Nonlinear Dynamics and Chaos. Addison-Wesley.

Distributed material.

If the course is discontinued, students may request to be examined during the following two academic years.

• INL1 - Assignment, 3.5 credits, grading scale: P, F
• TEN1 - Oral exam, 4.0 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.

INL1 Assignment 3,5 (P,F)

TEN1 Oral exam 4,0 (P, F)

Homework assignments and oral exam.

Arne Nordmark

• 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.