M6201 Non-linear dynamics

Faculty of Science
Spring 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:
M6201/01: Wed 12:00–13:50 MP2,01014a, 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
there are 11 fields of study the course is directly associated with, display
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
The course is also listed under the following terms Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2016, spring 2018, Spring 2022, Spring 2024.
  • Enrolment Statistics (Spring 2020, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2020/M6201