PřF:M6201 Non-linear dynamics - Course Information
M6201 Non-linear dynamics
Faculty of ScienceSpring 2014
- 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
- Thu 14:00–15:50 M2,01021
- Timetable of Seminar Groups:
M6201/02: Mon 8:00–9:50 MP1,01014, L. Přibylová - 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
- Applied Mathematics for Multi-Branches Study (programme PřF, B-MA)
- Applied Mathematics for Multi-Branches Study (programme PřF, N-MA)
- Economics (programme ESF, N-MA)
- Financial and Insurance Mathematics (programme PřF, B-MA)
- Finance Mathematics (programme PřF, N-MA)
- Mathematical Biology (programme PřF, B-EXB)
- Mathematical Biology (programme PřF, N-EXB)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Modelling and Calculations (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, N-MA)
- Course objectives
- The aim of the course is to present introduction to nonlinear dynamics of continuous and discrete models. Students will be able to explain one and multiparametric bifurcations and chaotic dynamics. Students should be able to illustrate mentioned nonlinear phenomena in models from various science fields (biology, biochemistry, physics, ecology, economy etc.)
- Syllabus
- Basic concepts: dynamical systems, nonlinear autonomous systems, parameter dependence, continuous bifurcations (bifurcation saddle-node, hysteresis, Hopf bifurcation, reduction to central manifold, multiparametric bifurcations), discrete bifurcations (fold, flip, period doubling and universality, deterministic chaos, Neimark-Sacker bifurcation), Poincaré section and bifurcations of cycles, chaos in continuous systems.
- Literature
- required literature
- PŘIBYLOVÁ, Lenka. Nelineární dynamika a její aplikace. 1. vyd. Brno: Masarykova univerzita, 2012. Elportál. ISBN 978-80-210-5969-6. URL info
- recommended literature
- 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. In class exercises active participation of students is required.
- Assessment methods
- Final examination contains of written test with computer usage and subsequent oral part, 50% of correct answers is needed to pass. Instead of this examination final project with presentation can be elected.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught once in two years.
- Enrolment Statistics (Spring 2014, recent)
- Permalink: https://is.muni.cz/course/sci/spring2014/M6201