Course: Discrete Dynamical Systems

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Course title Discrete Dynamical Systems
Course code KMA/DDSM
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Fišer Jiří, RNDr. Ph.D.
Course content
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.

Learning activities and teaching methods
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
Learning outcomes
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.
Differential calculus of functions of a single variable.

Assessment methods and criteria
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.
Recommended literature
  • P. N. V. Tu. (1994). Dynamical Systems. Springer, Berlin.
  • S. N. Elaydi. (1999). An Introduction to Difference Equations. Springer, New York.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Applied Mathematics (2014) Mathematics courses - Summer
Faculty of Science Mathematics and Applications (1) Mathematics courses 2 Summer