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Lecturer(s)
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Filip Radim, prof. Mgr. Ph.D.
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Kolář Michal, Mgr. Ph.D.
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Course content
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1. One-Dimensional (1D) Systems: flows on the line, fixed points, linear stability 2. Bifurcations: saddle-node, transcritical, and pitchfork 3. Nonlinear dynamics of laser and similar systems 4. Flows on the circle: uniform and nonuniform oscillator, overdamped pendulum, superconducting Josephson junction 5. Two-Dimensional (2D) Systems: basic notions, classifications 6. Phase plane: linear systems, classification of fixed points, phase portraits, conservative and reversible systems 7. Limit cycles and Poincaré-Bendixson theorem: Lienard systems and relaxation oscillations 8. Bifurcations in 2D: Hopf bifurcations, and global bifurcations of cycles, hysteresis in Josephson junction 9. Chaos: Lorenz equations, strange attractors, period doubling, examples in physics.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
- Preparation for the Exam
- 13 hours per semester
- Homework for Teaching
- 26 hours per semester
- Attendace
- 52 hours per semester
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Learning outcomes
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The goal of the course is to introduce basic nonlinear dynamics and chaotic systems and their practical application in physics. Students will be able to learn numerical simulations of nonlinear systems, their analysis, and control.
Focused on acquiring knowledge. Define key concepts, describe key approaches, and demonstrate theoretical knowledge for solving model problems.
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Prerequisites
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Knowledge of differential equations, probability theory, mechanics, theoretical mechanics, electric circuits, quantum mechanics.
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Assessment methods and criteria
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Oral exam, Written exam, Student performance
Knowledge within the scope of the course topics.
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Recommended literature
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& Haken, H. (1981). Chaos and order in nature. Berlin.
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Haken, H. (1978). Synergetics: an introduction ; nonequilibrium phase and self-organization in physics, chemistry and biology. Berlin.
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Horák, J., Krlín, L., & Raidl, A. (2003). Deterministický chaos a jeho fyzikální aplikace. Praha.
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Horák, J., Krlín, L., & Raidl, A. (2007). Deterministický chaos a podivná kinetika. Praha.
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Peitgen, H. O., Jürgens, H., & Saupe, D. (2004). Chaos and fractals: new frontiers of science. New York, N.Y.
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Steven H. Strogatz. (2014). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Boca Raton.
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