# FSG3045 Non-linear Oscillations and Dynamical Systems 7.5 credits

The student is made familiar with phenomena appearing in nonlinear dynamics and is required to perform certain analysis of nonlinear models with analytical and numerical methods.

Course offering missing for current semester as well as for previous and coming semesters
Headings with content from the Course syllabus FSG3045 (Spring 2019–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

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

### Intended learning outcomes

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.

### Course disposition

No information inserted

## Literature and preparations

### Specific prerequisites

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

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

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

Distributed material.

## Examination and completion

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

P, F

### Examination

• 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)

### Other requirements for final grade

Homework assignments and oral exam.

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### 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 web

No information inserted

SCI/Mechanics

### Main field of study

This course does not belong to any Main field of study.

Third cycle