SubjectsSubjects(version: 853)
Course, academic year 2019/2020
  
Numerical methods of Analysis of Non-linear Dynamical Models - P413005
Title: Numerické metody analýzy nelineárních dynamických modelů
Guaranteed by: Department of Mathematics (413)
Actual: from 2019
Semester: both
Points: 0
E-Credits: 0
Examination process:
Hours per week, examination: 3/0 other [hours/week]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Level:  
For type: doctoral
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.
Interchangeability : D413006
Annotation -
Last update: Kubíček Milan prof. RNDr. CSc. (27.09.2018)
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.
Aim of the course -
Last update: Kubíček Milan prof. RNDr. CSc. (27.09.2018)

Solutions of projects, oral examination.

Literature -
Last update: Axmann Šimon Mgr. Ph.D. (12.10.2018)

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).

Teaching methods -
Last update: Kubíček Milan prof. RNDr. CSc. (27.09.2018)

Self-study, consultations.

Syllabus -
Last update: Kubíček Milan prof. RNDr. CSc. (27.09.2018)

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.

Entry requirements -
Last update: Borská Lucie RNDr. Ph.D. (16.09.2019)

Mathematics A, B; Mathematics for Chemical Engineers

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (16.09.2019)

none

Course completion requirements -
Last update: Kubíček Milan prof. RNDr. CSc. (27.09.2018)

Solutions of projects, oral examination.

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

 
VŠCHT Praha