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Lecturer(s)
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Tomeček Jan, doc. RNDr. Ph.D.
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Course content
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1. First order dynamical systems. 2. Points of equilibrium (critical points). 3. Stability. 4. Criteria of the asymptotic stability. 5. Periodic points and cycles. 6. The logistic equation and bifurcations. 7. Applications. 8. Dynamical systems of higher order.
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Learning activities and teaching methods
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Lecture, Projection (static, dynamic)
- Attendace
- 52 hours per semester
- Preparation for the Course Credit
- 20 hours per semester
- Preparation for the Exam
- 50 hours per semester
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Learning outcomes
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Students will have acquired a basic understanding of discrete time dynamical systems on the interval.
Comprehension Students will have acquired a basic understanding of discrete time dynamical systems on the interval; be able to find the fixed and periodic points of simple dynamical systems on the interval, and determine their stability; have some familiarity with some of the simpler bifurcations that fixed and periodic points can undergo; have some familiarity with the notion of self-similar fractals, and how they arise as attractors.
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Prerequisites
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Differential calculus of functions of a single variable.
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Assessment methods and criteria
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Mark, Oral exam, Written exam
Credit: the student has to obtain at least half of the possible points in a written test. Exam: the student has to understand the subject.
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Recommended literature
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A. S. A. Johnson, K. M. Madden, A. A. Sahin. (2017). Discovering Discrete Dynamical Systems. Mathematical Association of America.
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Andres, J., Fišer, J., & Rypka, M. (2015). Dynamické systémy 3: úvod do teorie deterministického chaosu a fraktální geometrie.
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C. Robinson. (1998). Dynamical Systems: Stability, Symbolic Dynamics, and Chaos. 2. edition. CRC Press, Boca Raton.
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P. N. V. Tu. (1994). Dynamical Systems. Springer, Berlin.
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S. N. Elaydi. (2005). An Introduction to Difference Equations. Springer, New York.
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