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Bifurcation phenomena in nonlinear dynamic systems. Branching of equilibrium states in the solution diagram,
continuation, branch points, Hopf bifurcation, bifurcation diagram. Calculation of periodic solutions and their stability,
continuation. Evolution diagram. Calculation of Ljapunov exponents using variational equations and fractal dimensions of
attractor from time series. Numerical methods for analyzing systems with distributed parameters.
Last update: Kubíček Milan (27.09.2018)
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Solutions of projects, oral examination. Last update: Kubíček Milan (27.09.2018)
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Solutions of projects, oral examination. Last update: Kubíček Milan (27.09.2018)
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Kubíček M., Marek M,: Computational Methods in Bifurcation Theory and Dissipative Systems. Springer, New York (1983). Holodniok M., Klíč A., Kubíček M., Marek M.: Metody analýzy nelineárních dynamických modelů (1986). Kuznetsov Y.: Elements of Applied Bifurcation Theory (2004). Teschl G.: Ordinary Differential Equations and Dynamical Systems (2012). Last update: Axmann Šimon (12.10.2018)
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Self-study, consultations. Last update: Kubíček Milan (27.09.2018)
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1. Lumped parameter systems. Examples.
2. Continuation algorithm.
3. Diagram of stationary solutions.
4. Stability of stationary solutions.
5. Branching of stationary solutions.
6. Hopf's bifurcation.
7. Construction of bifurcation diagram.
8. Methods of dynamic simulation and construction of phase portrait.
9. Calculation and continuation of periodic solutions.
10. Branching of periodic solutions.
11. Characterization of chaotic attractors.
12. Non-autonomous systems.
13. Selected methods for analyzing distributed parameters systems.
14. Primary and secondary bifurcations. Last update: Kubíček Milan (27.09.2018)
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Mathematics A, B; Mathematics for Chemical Engineers Last update: Borská Lucie (16.09.2019)
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none Last update: Borská Lucie (16.09.2019)
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