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Methods of Analysis of Non-linear Dynamical Models - S409001

Title:	Methods of Analysis of Non-linear Dynamical Models
Guaranteed by:	Department of Chemical Engineering (409)
Faculty:	Faculty of Chemical Engineering
Actual:	from 2019
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
Teaching methods:	full-time
Level:
For type:
Note:	course can be enrolled in outside the study plan enabled for web enrollment

Guarantor:	Schreiber Igor prof. Ing. CSc.

Examination dates Schedule

Annotation

Last update: Schreiber Igor prof. Ing. CSc. (13.02.2014)

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: SMIDOVAL (13.02.2014)

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: SMIDOVAL (13.02.2014)

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: SMIDOVAL (13.02.2014)

http://www.vscht.cz/mat/Ang/indexAng.html

Teaching methods

Last update: SMIDOVAL (13.02.2014)

Lectures and exercise classes.

Syllabus

Last update: SMIDOVAL (13.02.2014)

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: SMIDOVAL (13.02.2014)

Mathematics I, Mathematics for chemical engineers

Course completion requirements

Last update: SMIDOVAL (13.02.2014)

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