FY8910 - Nonlinear Dynamics
Lessons are not given in the academic year 2017/2018
Graphical solution methods for non-linear differential equations. Phase portraits, fixed point analysis, bifurcations, limit cycles, strange attractors, Poincare and Lorenz maps, multiscale perturbation theory. Iterative maps. Period doubling, chaos, scaling and universality. Fractals. Physical examples.
The course is an introduction to nonlinear systems and chaos. The student is expected to acquire basic knowledge of nonlinear differential equations and iterative maps. The student is capable of
finding fixed points and determine their stability, analyze the various
types of bifurcations in one dimension (saddle node, transcritical, and pitchfork) and two dimensions (homoclinic, degenerate, and Hopf),
draw bifurcation diagrams and stability diagrams. For two-dimensional systems, the student is able to draw phase portraits and find basins of attraction. Moreover, the student is able to analyze limit cycles and their stability.
The student can analyze discrete maps, find their fixed points and
understand the mechanism behind period doubling. The student has basic knowledge of the most important fractals, and their topological and metric properties. Similarly, the student knows about the properties of the most important strange attractors in discrete and continuous time. The students will improve their communication skills by solving problems on the blackboard and training in solving nonlinear problems using numerical methods.
Learning methods and activities
Given every other year, next time fall 2018.
Lectures and problem sessions. All students will go through a set of exercises on the blackboard during the semester, to be allowed to take the exam. In addition, all students must solve a numerical assignment and hand in a report. A re-sit exam in August may be changed from written to oral.
Exam registration requires that class registration is approved in the same semester. Compulsory activities from previous semester may be approved by the department.
Recommended previous knowledge
Basic university level physics and mathematics. The course is suitable for students in other departments, provided they have a good background in mechanics and mathematics.
Steven H. Strogatz: Nonlinear Dynamics and Chaos.
- * The location (room) for a written examination is published 3 days before examination date.