SubjectsSubjects(version: 953)
Course, academic year 2021/2022
Numerical methods of Analysis of Non-linear Dynamical Models - P413005
Title: Numerické metody analýzy nelineárních dynamických modelů
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2021 to 2022
Semester: both
Points: 0
E-Credits: 0
Examination process:
Hours per week, examination: 3/0, other [HT]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Note: course is intended for doctoral students only
can be fulfilled in the future
you can enroll for the course in winter and in summer semester
Guarantor: Kubíček Milan prof. RNDr. CSc.
Axmann Šimon Mgr. Ph.D.
Annotation -
Bifurcation phenomena in nonlinear dynamic systems. Branching of equilibrium states in the solution diagram, continuation, branch points, Hopf bifurcation, bifurcation diagram. Calculation of periodic solutions and their stability, continuation. Evolution diagram. Calculation of Ljapunov exponents using variational equations and fractal dimensions of attractor from time series. Numerical methods for analyzing systems with distributed parameters.
Last update: Kubíček Milan (27.09.2018)
Aim of the course -

Solutions of projects, oral examination.

Last update: Kubíček Milan (27.09.2018)
Literature -

Kubíček M., Marek M,: Computational Methods in Bifurcation Theory and Dissipative Systems. Springer, New York (1983).

Holodniok M., Klíč A., Kubíček M., Marek M.: Metody analýzy nelineárních dynamických modelů (1986).

Kuznetsov Y.: Elements of Applied Bifurcation Theory (2004).

Teschl G.: Ordinary Differential Equations and Dynamical Systems (2012).

Last update: Axmann Šimon (12.10.2018)
Teaching methods -

Self-study, consultations.

Last update: Kubíček Milan (27.09.2018)
Syllabus -

1. Lumped parameter systems. Examples.

2. Continuation algorithm.

3. Diagram of stationary solutions.

4. Stability of stationary solutions.

5. Branching of stationary solutions.

6. Hopf's bifurcation.

7. Construction of bifurcation diagram.

8. Methods of dynamic simulation and construction of phase portrait.

9. Calculation and continuation of periodic solutions.

10. Branching of periodic solutions.

11. Characterization of chaotic attractors.

12. Non-autonomous systems.

13. Selected methods for analyzing distributed parameters systems.

14. Primary and secondary bifurcations.

Last update: Kubíček Milan (27.09.2018)
Entry requirements -

Mathematics A, B; Mathematics for Chemical Engineers

Last update: Borská Lucie (16.09.2019)
Registration requirements -


Last update: Borská Lucie (16.09.2019)
Course completion requirements -

Solutions of projects, oral examination.

Last update: Kubíček Milan (27.09.2018)