SubjectsSubjects(version: 912)
Course, academic year 2021/2022
Methods of Analysis of Non-linear Dynamical Models - N413012
Title: Metody analýzy nelineárních dynamických modelů
Guaranteed by: Department of Mathematics (413)
Faculty: Faculty of Chemical Engineering
Actual: from 2020
Semester: summer
Points: summer s.:5
E-Credits: summer s.:5
Examination process: summer s.:
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
For type:  
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Kubíček Milan prof. RNDr. CSc.
Is interchangeable with: M413006
Examination dates   Schedule   
Annotation -
Last update: Kubíček Milan prof. RNDr. CSc. (01.08.2013)
The course is oriented on ability of formulation of nonlinear dynamical models in the form of systems of ordinary differential equations. Continuation of steady state solutions in dependence on a parameter, construction of solution diagram, bifurcation diagram and their interpretation. Bifurcation of steady states, Hopf bifurcation. Continuation and bifurcation of periodic solutions in dependence on a parameter. Selected engineering and physical problems are solved.
Aim of the course -
Last update: Kubíček Milan prof. RNDr. CSc. (01.08.2013)

Students will be able to analyze dynamic behaviour of the model described by a system of ordinary differential equations in dependence on parameters.

Literature -
Last update: Kubíček Milan prof. RNDr. CSc. (01.08.2013)

R: Kubíček M., Marek M.: Computational Methods in Bifurcation Theory and Dissipative Structures. Springer Verlag, New York 1983. ISBN 0-387-12070-X.

A: Individually according to the project orientation.

Learning resources -
Last update: Kubíček Milan prof. RNDr. CSc. (27.08.2013)

Teaching methods -
Last update: TAJ413 (01.08.2013)

Lectures and exercise classes.

Syllabus -
Last update: TAJ413 (04.10.2005)

1. Lumped parameter systems. Examples.

2. Continuation algorithm.

3. Diagram of steady state solutions.

4. Stability of steady state solutions.

5. Branching of steady state solutions.

6. Hopf bifurcation.

7. Construction of bifurcation diagram.

8. Simulation methods and construction of phase portrait.

9. Computation and continuation of periodic solutions.

10. Bifurcation of periodic solutions.

11. Characterization of chaotic attractors.

12. Nonautonomous systems.

13. Selected methods for analysis of distributed parameter systems.

14. Primary and secondary bifurcation.

Registration requirements -
Last update: Kubíček Milan prof. RNDr. CSc. (01.08.2013)

Mathematics I, Mathematics for chemical engineers

Course completion requirements
Last update: TAJ413 (11.07.2013)

Z: Holodniok M., Klíč A., Kubíček M., Marek M.: Metody analýzy nelineárních dynamických modelů. Academia Praha 1986. ISBN 21-010-86.

D: dodávána individuálně podle zaměření projektu

Teaching methods
Activity Credits Hours
Konzultace s vyučujícími 0,5 14
Obhajoba individuálního projektu 0,5 14
Účast na přednáškách 1 28
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 1 28
Práce na individuálním projektu 0,5 14
Příprava na zkoušku a její absolvování 1 28
Účast na seminářích 0,5 14
5 / 5 140 / 140
Coursework assessment
Form Significance
Regular attendance 10
Defense of an individual project 20
Examination test 20
Continuous assessment of study performance and course -credit tests 10
Oral examination 40