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Last update: Dubcová Miroslava RNDr. Ph.D. (18.07.2013)
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Last update: Dubcová Miroslava RNDr. Ph.D. (18.07.2013)
Students should be able to describe autonomous systems of differential equations qualitatively. Namely, they should be able to determine stability of solutions, to recognize chaotic attractor and to classify bifurcations. |
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Last update: TAJ413 (28.08.2013)
R: A. Klíč, M. Dubcová,L. Buřič: Soustavy obyčejných diferenciálních rovnic, kvalitativní teorie, dynamické systémy, VŠCHT Praha, 2009, ISBN: 978-80-7080-724-8 R: R.C.Robinson: An Introduction to Dynamical Systems: Continuous and Discrete. Pearson Prentice Hall, 2004, ISBN 0-13-143140-4 A: M. W. Hirsch, S. Smale, R. L. Devaney: Differencial Equations, Dynamical Systems & An Introductions to Chaos, Elsevier 2004, ISBN0-12-349703-5 |
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Last update: Dubcová Miroslava RNDr. Ph.D. (18.07.2013)
http://www.vscht.cz/mat/SODR/E-collection/SbirkaDR-Ang.pdf |
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Last update: TAJ413 (19.07.2013)
Lectures and exercise classes. |
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Last update: Dubcová Miroslava RNDr. Ph.D. (18.07.2013)
1. The concept of dynamical systems. Continuous and discrete dynamical systems. 2. Autonomous systems of ODEs. Qualitative approach. Phase flow. The notion of stability. 3. Attractor. 4. Planar systems. Phase portraits of linear systems. 5. Phase portraits of nonlinear systems. Grobman-Hartman theorem. 6. First integrals and applications. 7. Phase portraits of linear and nonlinear systems in R^3. 8. Stability theory. Poincare mapping. 9. Nonautonomous systems of ODEs. 10. Periodic linear systems. Monodromy matrix. Floquet theory. 11. Systems of ODEs depending on parameters. Bifurcations. 12. Examples: "Brusselator", Lorenz system, dumped oscillator. 13. Discrete dynamical systems, basic notions. 14. Regular and chaotic behavior. Lyapunov exponents. |
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Last update: TAJ413 (16.07.2013)
Mathematics I, Mathematics II |
Teaching methods | ||||
Activity | Credits | Hours | ||
Konzultace s vyučujícími | 0.5 | 14 | ||
Účast na přednáškách | 1 | 28 | ||
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi | 0.5 | 14 | ||
Příprava na zkoušku a její absolvování | 2 | 56 | ||
Účast na seminářích | 1 | 28 | ||
5 / 5 | 140 / 140 |
Coursework assessment | |
Form | Significance |
Regular attendance | 10 |
Examination test | 35 |
Continuous assessment of study performance and course -credit tests | 20 |
Oral examination | 35 |