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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.
Poslední úprava: Schreiber Igor (13.02.2014)
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Students will be able to analyze dynamic behaviour of the model described by a system of ordinary differential equations in dependence on parameters. Poslední úprava: SMIDOVAL (13.02.2014)
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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. Poslední úprava: SMIDOVAL (13.02.2014)
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http://www.vscht.cz/mat/Ang/indexAng.html Poslední úprava: SMIDOVAL (13.02.2014)
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Lectures and exercise classes. Poslední úprava: SMIDOVAL (13.02.2014)
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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. Poslední úprava: SMIDOVAL (13.02.2014)
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Mathematics I, Mathematics for chemical engineers Poslední úprava: SMIDOVAL (13.02.2014)
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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 Poslední úprava: SMIDOVAL (13.02.2014)
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