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Numerical methods of Analysis of Non-linear Dynamical Models - AP413005

Title:	Numerical methods of Analysis of Non-linear Dynamical Models
Guaranteed by:	Department of Mathematics, Informatics and Cybernetics (446)
Faculty:	Faculty of Chemical Engineering
Actual:	from 2021
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:	English
Teaching methods:	full-time
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: Pátková Vlasta (16.11.2018)

Aim of the course -

Solutions of projects, oral examination.

Last update: Pátková Vlasta (16.11.2018)

Course completion requirements -

Solutions of projects, oral examination.

Last update: Pátková Vlasta (16.11.2018)

Literature -

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

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

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

Last update: Jahoda Milan (28.11.2018)

Teaching methods -

Self-study, consultations.

Last update: Pátková Vlasta (16.11.2018)

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: Pátková Vlasta (16.11.2018)

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)