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Deterministic Chaos and Fractals [EN]

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Erasmus code / ISCED: 13.2 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (unknown)
Course title: Deterministic Chaos and Fractals [EN]
Name in Polish: Deterministic Chaos and Fractals
Organizational unit: Faculty of Mathematics and Natural Sciences. School of Exact Sciences.
Course groups: Courses at UKSW
Course homepage:
ECTS credit allocation (and other scores): 6.00 OR 5.00 (depends on study program) Basic information on ECTS credits allocation principles:
  • the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS;
  • the student’s weekly hourly workload is 45 h;
  • 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes;
  • weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS;
  • work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load.

view allocation of credits
Language: English
Subject level:


Learning outcome code/codes:

enter learning outcome code/codes





Short description:

Basic properties of dynamical systems

Deterministic chaos, strange attractors, and fractals

Bifurcations and intermittency

Applications for analysis of various complex systems in nature and in economy

Full description:

Dynamical View of Nature

Fractals: Cantor Set

Stability of Linear Systems

Attracting and Stable Fixed Points

Nonlinear Systems: Pendulum

Strange Attractors and Deterministic Chaos

Bifurcations and Intermittency

Stretching and Folding Mechanism

Baker's Map

Logistic Map

Henon Map

Lorenz System

Generalized Dimensions


Quantum Chaos


S. H. Strogatz, Nonlinear Dynamics and Chaos,

Addison-Wesley, Reading, 1994.

E. Ott, Chaos in Dynamical Systems,

Cambridge University Press, 1993.

Efekty kształcenia i opis ECTS:

On successful completion of this course student should know basics of fractal analysis and dynamics of linear and nonlinear systems.

The student is able to evaluate importance of nonlinearity in mathematical models.

He should be able to apply suitable theoretical models to fractal analysis of real nonlinear systems.

The student should understand practical importance of the acquired knowledge.

Assessment methods and assessment criteria:

Written exam (test) and exercises.

Classes in period "Summer semester 2019/20" (past)

Time span: 2020-02-01 - 2020-09-20
Choosen plan division:

see course schedule
Type of class:
Classes, 30 hours more information
Lectures, 30 hours more information
Coordinators: Wiesław Macek
Group instructors: Wiesław Macek
Students list: (inaccessible to you)
Examination: examination
(in Polish) E-Learning:

(in Polish) E-Learning (pełny kurs) z podziałem na grupy

Type of subject:


(in Polish) Grupa przedmiotów ogólnouczenianych:

(in Polish) nie dotyczy

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