Subjects

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Numerical methods of Analysis of Non-linear Dynamical Models - P413005

Title:	Numerické metody analýzy nelineárních dynamických modelů
Guaranteed by:	Department of Mathematics (413)
Faculty:	Faculty of Chemical Engineering
Actual:	from 2019 to 2020
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
Level:
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.
Classification:	Mathematics > Mathematics General

Examination dates Schedule

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)

Course completion requirements -

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)

Learning outcomes -

Solutions of projects, oral examination.

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 -

none

Last update: Borská Lucie (16.09.2019)

Coursework assessment
Form	Significance
Defense of an individual project	30
Oral examination	70