FYS-2013 Chaos, fractals and complexity

Work Load 10  credits (ECTS)

Type of course Theoretical and practical subject.

Level of course/Year of study Normally third year.

Language of instruction Norwegian, or English by request

Examination semester Autumn

Contents The course gives an introduction to modern methods for studying low-dimensional dynamical systems with chaotic behaviour and for systems with a high degree of complexity. The subject is cross-disciplinary and the course presents applications from mechanics, electronics, meteorology, chemistry, biology, geology, and economics. Material taught is: One-dimensional maps, one-dimensional linear and non-linear ordinary differential equations and their numerical solutions, theory for dynamical systems with attractors for chaotic dissipative flows, Lyapunov exponents, bifurcations, Hamiltonian chaos, time-series analysis, fractals and estimates of fractal dimension of stochastic signals, complex systems with simulation of cellular automata, and study of self-organized criticality. Successful completition of the course requires that the student has the knowledge corresponding to basic calculus and linear algebra and an introductory college course in general physics. Some knowledge in statistics and programming is also an advantage. Course material and computer projects will be presented as Mathematica notebooks, so some experience with Mathematica is also an advantage. The student can use other programming tools, like MATLAB, for the projects if the wish to do so.

Recommended previous qualifications FYS-0100 Basic physics, MAT-1001 Calculus 1, MAT-1002 Calculus 2, MAT-1004 Linear algebra

Form of teaching The teaching consists of lectures (40 h) and practice classes (40 h). The practice will basically consist of weekly computerprojects which are initiated during the classes and are finished as homework. The homework reports will be handed in and used in the final evaluation.

Exam and assessment Portfolio assessment of the weekly computerprojects combined with a final oral examination concentrated on the projects. Grading scale: A-F. Re-sit examination: Early in tutor free term, with reserve of postponed examination, handing in of revised computerproject combined with an oral examination concentrating on the projects. Postponed examination: According to the current regulation of exams § 21. New examination: According to the current regulation exams § 25, last paragraph.

Contact person/lecturer Student counsellor Geir Antonsen Phone: +47 77 64 54 76, e-mail: stud-kons@phys.uit.no

Recommended reading/syllabus Available on request