SubjectsSubjects(version: 923)
Course, academic year 2022/2023
Methods of Analysis of Non-linear Dynamical Models - M413006
Title: Metody analýzy nelineárních dynamických modelů
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2021
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
Language: Czech
Teaching methods: full-time
For type:  
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
This subject contains the following additional online materials
Annotation -
Last update: Hladíková Jana (16.01.2018)
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: Hladíková Jana (16.01.2018)

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: Hladíková Jana (16.01.2018)

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: Hladíková Jana (16.01.2018)

Teaching methods -
Last update: Hladíková Jana (16.01.2018)

Lectures and exercise classes.

Syllabus -
Last update: Hladíková Jana (16.01.2018)

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.

Entry requirements -
Last update: Borská Lucie RNDr. Ph.D. (13.05.2019)

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.

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (06.05.2019)

No requirements.

Course completion requirements
Last update: Hladíková Jana (16.01.2018)

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