Lecturer(s)


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 selfsimilar fractals, and how they arise as attractors.

Prerequisites

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.
