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Lecturer(s)
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Krajščáková Věra, Mgr.
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Tomeček Jan, doc. RNDr. Ph.D.
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Rachůnková Irena, prof. RNDr. DrSc.
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Course content
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1. Modelling using dynamical systems. 2. Linear systems, classification. 3. Nonlinear systesm, local theory. Stability. 4. Gradient and hamiltonian systems. 5. 2D models: Bifurcations and limit cycles (Poincaré-Bendixson theory), Lotka-Volterra model, pendulum, oscilators. 6. 3D models: chaos and strange attractors (Rosler, Lorenz).
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Learning activities and teaching methods
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Lecture
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Learning outcomes
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Understand basic notions concerning dynamical systems.
Comprehension Understand basic notions concerning dynamical systems.
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Prerequisites
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Differential and integral calculus.
KMA/MA1 and KAG/LA1A
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Assessment methods and criteria
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Oral exam, Seminar Work
Oral exam. Credits: defense of the seminal work
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Recommended literature
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Online přednáška.
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F. Verhulst. (1990). Nonlinear Differential Equations and Dynamical Systems. Springer-Verlag, Berlin.
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J. Hale, H. Kocak. (1991). Dynamics and Bifurcation. Springer-Verlag, New York.
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Katok, A.; Hasselblatt, B. (1995). Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press, Cambridge.
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Rachůnková, J. Fišer. (2014). Dynamické systémy 1. UP v Olomouci, Olomouc.
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S. Strogatz. (2014). Nonlinear Dynamics and Chaos, With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity). Avalon Publishing.
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