SubjectsSubjects(version: 953)
Course, academic year 2019/2020
Methods of Analysis of Non-linear Dynamical Models - M413006
Title: Metody analýzy nelineárních dynamických modelů
Guaranteed by: Department of Mathematics (413)
Faculty: Faculty of Chemical Engineering
Actual: from 2019 to 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: unlimited / unlimited (unknown)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Kohout Martin Ing. Ph.D.
Axmann Šimon Mgr. Ph.D.
Interchangeability : N413012
Examination dates   Schedule   
This subject contains the following additional online materials
Annotation -
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.
Last update: Hladíková Jana (16.01.2018)
Aim of the course -

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

Last update: Hladíková Jana (16.01.2018)
Literature -

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.

Last update: Hladíková Jana (16.01.2018)
Learning resources -

Last update: Hladíková Jana (16.01.2018)
Teaching methods -

Lectures and exercise classes.

Last update: Hladíková Jana (16.01.2018)
Syllabus -

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.

Last update: Hladíková Jana (16.01.2018)
Entry requirements -

Students are expected to have either completed at least one of the prerequisite courses Mathematics for chemical engineers or Systems of ordinary differential equations or possess the equivalent knowledge on linear dynamical systems prior to enrolling in the course.

Last update: Borská Lucie (13.05.2019)
Registration requirements -

No requirements.

Last update: Borská Lucie (06.05.2019)
Course completion requirements

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

Last update: Hladíková Jana (16.01.2018)
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