M6201 Non-linear dynamics

Faculty of Science
spring 2012 - acreditation

The information about the term spring 2012 - acreditation is not made public

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
Prerequisites
Any course of calculus and linear algebra.
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
Course objectives
The aim of the course is to present introduction to nonlinear dynamics of continuous and discrete models, explain one and multiparametric bifurcations and chaotic dynamics. Mentioned nonlinear phenomena will be illustrated in models from various science fields (biology, biochemistry, physics, ecology, economy etc.)
Syllabus
  • Basic concepts: dynamical systems, nonlinear autonomous systems, parameter dependence, continuous bifurcations (bifurkace saddle-node, hysteresis, Hopf bifurcation, reduction to central manifold, multiparametric bifurcations), discrete bifurcations (fold, flip, period doubling a universality, deterministic chaos, Neimark-Sacker bifurcation), Poincaré section a bifurcations of cycles, chaos in continuous systems.
Literature
  • Studijní materiál v e-learningové podobě vytvoření pro předmět přednášející.
  • KUZNECOV, Jurij Aleksandrovič. Elements of applied bifurcation theory. 2nd ed. New York: Springer-Verlag, 1998, xviii, 591. ISBN 0387983821. info
  • CHOW, Shui-Nee and Jack K. HALE. Methods of bifurcation theory. 2nd corr. print. New York: Springer-Verlag, 1996, xv, 525 s. ISBN 0-387-90664-9-. info
Teaching methods
Two hours of theoretical lecture and two hours of class exercises weekly. Seminary requires active participation of students.
Assessment methods
final exam contains written test and subsequent oral part.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2012, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.