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Course info
OPT / SYN
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Course description
Department/Unit / Abbreviation
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OPT
/
SYN
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Academic Year
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2024/2025
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Academic Year
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2024/2025
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Title
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Nonlinear Dynamics, Chaos & Synergetics
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Form of course completion
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Exam
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Form of course completion
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Exam
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Long Title
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Nonlinear Dynamics, Chaos and Synergetics
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Accredited / Credits
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Yes,
5
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
3
[Hours/Week]
Exercise
1
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech, English
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Occ/max
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|
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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not determined
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech, English
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
A|B|C|D|E|F |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
Yes
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Fundamental course |
No
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Fundamental theoretical course |
Yes
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Evaluation scale |
A|B|C|D|E|F |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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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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Requirements on student
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Knowledge within the scope of the course topics.
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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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Activities
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Fields of study
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Guarantors and lecturers
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-
Guarantors:
prof. Mgr. Radim Filip, Ph.D. (100%),
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Lecturer:
prof. Mgr. Radim Filip, Ph.D. (100%),
Mgr. Michal Kolář, Ph.D. (100%),
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Tutorial lecturer:
prof. Mgr. Radim Filip, Ph.D. (100%),
Mgr. Michal Kolář, Ph.D. (100%),
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Seminar lecturer:
prof. Mgr. Radim Filip, Ph.D. (100%),
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Literature
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Basic:
& Haken, H. (1981). Chaos and order in nature. Berlin: Springer.
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Basic:
Steven H. Strogatz. (2014). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Boca Raton.
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Basic:
Haken, H. (1978). Synergetics: an introduction ; nonequilibrium phase and self-organization in physics, chemistry and biology. Berlin: Springer.
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Recommended:
Horák, J., Krlín, L., & Raidl, A. (2003). Deterministický chaos a jeho fyzikální aplikace. Praha: Academia.
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Recommended:
Horák, J., Krlín, L., & Raidl, A. (2007). Deterministický chaos a podivná kinetika. Praha: Academia.
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Recommended:
Peitgen, H. O., Jürgens, H., & Saupe, D. (2004). Chaos and fractals: new frontiers of science. New York, N.Y: Springer.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Preparation for the Exam
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13
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Attendace
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52
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Homework for Teaching
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26
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Total
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91
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Prerequisites - other information about course preconditions |
Knowledge of differential equations, probability theory, mechanics, theoretical mechanics, electric circuits, quantum mechanics. |
Competences acquired |
Předmět zaměřený na získávání znalostí. Definovat hlavní pojmy, popsat hlavní přístupy, prokázat teoretické znalosti pro řešení modelových problémů. |
Teaching methods |
- Lecture
- Work with Text (with Book, Textbook)
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Assessment methods |
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