M9BCF Bifurcation theory, chaos and fractals

Faculty of Science
Autumn 2022
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Zdeněk Pospíšil, Dr. (lecturer)
doc. RNDr. Lenka Přibylová, Ph.D. (lecturer)
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
Mon 14:00–15:50 M3,01023
  • Timetable of Seminar Groups:
M9BCF/01: Tue 12:00–13:50 MP2,01014a, L. Přibylová
Prerequisites
M5858 Continuous deterministic models I, M8230 Discrete deterministic models or M6201 Nonlinear dynamics and applications
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 summarize modern insight into one and multiparametric bifurcations and the concept, properties and rouths to deterministic chaos. Connections to typical nonlinear phenomena in various fields (biochemical switches and cycles, hysteresis and others) will be presented. Students will be able to use continuation software.
Learning outcomes
Students will be able to summarize modern methods of bifurcation theory, understand the concept and properties of deterministic chaos, explain typical rouths to chaos and connections with fractals. Students will be able to describe important nonlinear phenomena as biochemical switches, cycles or hysteresis. Students will be able to use continuation software.
Syllabus
  • Topological equivalence, homeomorphism and a method of normal forms, basic continuous one-parametric local bifurcations and their normal forms, multi-parametric continuous local bifurcations and their normal forms, non-local bifurcations, a method of reduction to the central manifold. Typical nonlinear phenomena (applied bifurcation theory in biochemistry, neuroscience etc.). Discrete local one-parametric bifurcations, period doubling and routes to deterministic chaos, real and complex insight to bifurcations of one-parametric maps, Mandelbrot set and its connection to chaotic dynamics. Chaos in continuous systems. Chaos in applications, chaos control, measure of chaos and methods to detect stable dynamics and transition to chaotic dynamics.
Literature
    recommended literature
  • KUZNECOV, Jurij Aleksandrovič. Elements of applied bifurcation theory. 2nd ed. New York: Springer-Verlag, 1998, xviii, 591. ISBN 0387983821. info
  • HILBORN, Robert C. Chaos and nonlinear dynamics : an introduction for scientists and engineers. New York: Oxford University Press, 1994, 654 s. ISBN 0195088166. info
  • STROGATZ, Steven H. Nonlinear dynamics and chaos : with applications to physics, biology, chemistry, and engineering. Cambridge, Mass.: Westview Press, 1994, xi, 498. ISBN 0738204536. info
Teaching methods
Two hours of theoretical lecture and two hours of computer class exercises weekly. In class exercises active participation of students is required.
Assessment methods
The conditions may be specified according to the evolution of the epidemiological situation and the legislative restrictions, it is assumed that the test will have a computer and oral part.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
General note: Střídá se s předmětem M6201.
The course is also listed under the following terms Autumn 2020, Autumn 2024.
  • Enrolment Statistics (Autumn 2022, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2022/M9BCF