PřF:M6201 Non-linear dynamics - Course Information
M6201 Non-linear dynamics
Faculty of ScienceSpring 2020
- 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)
RNDr. Veronika Eclerová, Ph.D. (assistant) - Guaranteed by
- prof. RNDr. Zdeněk Pospíšil, Dr.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Wed 10:00–11:50 M4,01024
- Timetable of Seminar Groups:
- 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.). Students will be able to analyze models in using appropriate software.
- Learning outcomes
- 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.) Students will be able to analyze models in using appropriate software.
- Syllabus
- Dynamical systems, nonlinear autonomous systems, parameter dependence, continuous bifurcations and applications (fold bifurcation, Hopf bifurcation, multiparametric bifurcations), discrete bifurcations and applications (fold, flip, period doubling and deterministic chaos), typical nonlinear phenomena (bistability, hysteresis, oscillations, transient dynamics, properties of chaotic dynamics), analysis of selected models.
- 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 (probably available only in Czech)
- Study Materials
The course is taught once in two years.
General note: Předpokládá se základní znalost lineární algebry a diferenciálního počtu. - Teacher's information
- https://is.muni.cz/auth/elearning/warp?kod=M6201;predmet=971300;zuv=589395;qurl=%2Fel%2F1431%2Fjaro2018%2FM6201%2Findex.qwarp;zpet=%2Fauth%2Fel%2F1431%2Fjaro2018%2FM6201%2Findex.qwarp%3Finfo;zpet_text=Zp%C4%9Bt%20do%20Spr%C3%A1vce%20soubor%C5%AF
- Enrolment Statistics (Spring 2020, recent)
- Permalink: https://is.muni.cz/course/sci/spring2020/M6201