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  Prospectuses 2011-2012
Radboud universityProspectusesFaculty of Science > Bachelor Wiskunde

Dynamic Systems 

Course ID
NWI-WB053B
Credits
3
Scheduled
fourth quarter
Teaching methods
  • 16 hrs lecture
  • 16 hrs problem session
Pre-requisites
Calculus 1, Calculus 2 (or comparable courses)

Objectives
  • The student is familiar with discrete dynamical systems, bifurcations and chaos.
  • The student is familiar with the one-parameter family of logistic functions and with the associated dynamical systems.
  • The student knows the theorem of Sarkovskii and is able to apply both the theorem and the most important ideas from its proof.
  • The studen is able to apply the method of topological conjugation, and in particular symbolic dynamics, to the study of the behavior of a dynamical system.
Contents
In this course the concept of a dynamical system, a systems which evolves discretely (or continuously) in time, will be introduced. Chaos will be made explicit in a mathematical way and will be studied by the logistic map. Chaos means a system is very sensitive for small changes in its initial conditions. The single most famous example is the one of the so-called butterfly effect: it claims a butterfly in Brazil would cause a tornado in Texas after several months, when the chaotic system of the weather has evolved. Also bifurcations will be studied. Bifurcation points are points in the initial parameters at which the evolution of the system suddenly changes. In addition to studying chaos Sarkovskii's theorem will be presented, which tells in what case one might expect chaos. Chaotic dynamical systems are of great importance for the study of fractals, natural processes in biology and applications in computer science. The discrete one-dimensional dynamical system corresponding to the logistic function will be studied.

Examination
Schriftelijk
Literature
: Robert L. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd ed., 1989, herdrukt in 2003.