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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. Nonlinear dynamics: nonlinear systems, stability, bifurcation, attractors, limit cycles, catastrophe, Ljapunov and asymptotic stability. 2. Chaotic dynamics of nonlinear systems: continuous Lorentz model, sensitivity on initial condition, strange attractors, Lorentz and Rossler attractor, Ljapunov exponents, discrete logistic model and population models, synchronization of chaotic systems. 3. Stochastic nonlinear systems: Langevin equations, master equation and Fokker-Planck equation, numerical simulations of nonlinear effects, phase transitions in nonlinear systems, self-organization. 4. Nonlinear dynamics in mechanics and electric circuits: periodically driven nonlinear pendulum, driven electric oscillator with nonlinear element, stabilization of nonlinear oscillators. 5. Nonlinear dynamics of laser: single mode laser, multi mode laser, phase transitions in laser, mode cooperation and concurrence in laser, chaos in laser dynamics. 6. Nonlinear dynamics in chemical and biological processes: deterministic processes, reaction and diffusion processes, population dynamics. 7. Practical simulation of nonlinear dynamics I (continuous systems) 8. Practical simulation of nonlinear dynamics II (discrete systems)
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Learning activities and teaching methods
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Lecture, 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 course is to introduce basic nonlinear dynamics and chaotic systems and their practical application in physics, chemistry and biology. Students will be able to practically learn numerical simulations of the nonlinear systems, their analysis and control.
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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
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: Springer.
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Haken, H. (1978). Synergetics: an introduction ; nonequilibrium phase and self-organization in physics, chemistry and biology. Berlin: Springer.
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Horák, J., Krlín, L., & Raidl, A. (2003). Deterministický chaos a jeho fyzikální aplikace. Praha: Academia.
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Horák, J., Krlín, L., & Raidl, A. (2007). Deterministický chaos a podivná kinetika. Praha: Academia.
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Peitgen, H. O., Jürgens, H., & Saupe, D. (2004). Chaos and fractals: new frontiers of science. New York, N.Y: Springer.
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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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