M6201 Non-linear dynamics

Faculty of Science
Spring 2012
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Lenka Přibylová, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Lenka Přibylová, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 8:00–9:50 M5,01013
  • Timetable of Seminar Groups:
M6201/01: Fri 13:00–14:50 MP1,01014
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 21 fields of study the course is directly associated with, display
Course objectives
At the end of the course students should get familiar with: elements of bifurcation theory of continuous and discrete dynamical systems; basic nonlinear phenomena in continuous and discrete dynamics; some chosen models of real processes that will illustrate the nonlinear phenomena
Syllabus
  • Dynamical systems (continuous and discrete)
  • Linear and nelinear systems
  • Systems dependent on parameters, bifurcations
  • One-parameter bifurcations in continuous case (bifurcation saddle-node, hysteresis, pitchfork, transcritical, Hopf bifurcation)
  • Multi-parameter bifurcation
  • Reduction to a central manifold
  • One-parameter bifurcations in discrete case (bifurcation fold, flip, period doubling and universality, deterministic chaos, Neimark-Sacker bifurcation)
  • Poincaré mapping and cycle bifurcation
  • Chaos in continuous systems
Literature
  • e-lerningový text přednášky na ISu
  • KUZNECOV, Jurij Aleksandrovič. Elements of applied bifurcation theory. 2nd ed. New York: Springer-Verlag, 1998, xviii, 591. ISBN 0387983821. info
Teaching methods
lectures followed by computer lab.
Assessment methods
Written exam followed by an oral one.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
The course is also listed under the following terms spring 2012 - acreditation, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.
  • Enrolment Statistics (Spring 2012, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2012/M6201