Nonlinear Dynamics
BASIC DATA
course listing
A - main register
course code
YFX1560
course title in Estonian
Mittelineaarne dünaamika
course title in English
Nonlinear Dynamics
course volume CP
-
ECTS credits
3.00
to be declared
yes
fully online course
not
assessment form
Examination
teaching semester
autumn - spring
language of instruction
Estonian
English
Study programmes that contain the course
code of the study programme version
course compulsory
yes
Structural units teaching the course
LT - Department of Cybernetics
Timetable link
Version:
VERSION SPECIFIC DATA
course aims in Estonian
Aine eesmärk on tutvustada üliõpilastele mittelineaarsusest tingitud mitteintuitiivset füüsikalist maailmapilti ning õpetada mittelineaarse dünaamika analüüsi meetodeid.
course aims in English
The aim of this course is to introduce students to nonintuitive physics caused by the nonlinearity of studied problems, and to teach the analysis methods of nonlinear dynamics.
learning outcomes in the course in Est.
Õppeaine läbinud üliõpilane:
- eristab ja analüüsib mittelineaarseid süsteeme ning kaootilisi režiime;
- seletab mittelineaarse dünaamika põhitõdesid ja termineid.
- eristab ja analüüsib mittelineaarseid süsteeme ning kaootilisi režiime;
- seletab mittelineaarse dünaamika põhitõdesid ja termineid.
learning outcomes in the course in Eng.
After completing this course, the student:
- recognises and analyses nonlinear systems and chaotic regimes;
- explains the fundamentals and concepts used in nonlinear dynamics.
- recognises and analyses nonlinear systems and chaotic regimes;
- explains the fundamentals and concepts used in nonlinear dynamics.
brief description of the course in Estonian
Mittelineaarne maailmapilt. Mittelineaarsed matemaatilised mudelid. Atraktorid. Bifurkatsioonid. Matemaatiliselt determineeritud kaos. Orbiidi ja Feigenbaumi diagrammid, Lorenz lõige, Poincaré lõige. Fraktaalsed struktuurid. Kujutised. Mandelbroti hulk ning Fatou ja Julia hulgad nende seos mittelineaarsete süsteemidega. Fraktaalsed dimensioonid. Kaootiliste protsesside identifitseerimine. Ljapunovi eksponent. Entroopia. Ennustatavuse horisont. Näited füüsikast, mehaanikast, bioloogiast ja ökoloogiast. Kaose teooria ja fraktaalse geomeetria rakendused.
brief description of the course in English
Nonlinearity and nonlinear world. Nonlinear mathematical models. Basic theory of ODEs and practical numerical integration. Attractors, bifurcations. Mathematically determined chaos. Orbit and the Feigenbaum diagrams, the Lorenz section, the Poincaré section. Fractality, fractal structures. Recurrence maps and feedback loops. The Mandelbrot set, and the Fatou and Julia sets their connection to nonlinear dynamical systems. Fractal dimensions. The universal route to chaos via period doubling cascade. Identification of chaotic processes. Analytical and numerical methods, the Lyapunov exponent. Entropy. Horizon of predictability. Examples from physics, mechanics, biology and ecology. Applications of chaos theory and fractal geometry.
type of assessment in Estonian
-
type of assessment in English
-
independent study in Estonian
-
independent study in English
-
study literature
S.H. Strogatz, Nonlinear Dynamics and Chaos With Applications to Physics, Biology, Chemistry, and Engineering, Second Edition, Avalon Publishing, 2014.
K.T. Alligood, T.D. Sauer, J.A. Yorke, Chaos: An Introduction to Dynamical Systems, Springer, 2000.
Ü. Lepik, J. Engelbrecht, Kaoseraamat, Teaduste Akadeemia Kirjastus, 1999.
K.T. Alligood, T.D. Sauer, J.A. Yorke, Chaos: An Introduction to Dynamical Systems, Springer, 2000.
Ü. Lepik, J. Engelbrecht, Kaoseraamat, Teaduste Akadeemia Kirjastus, 1999.
study forms and load
daytime study: weekly hours
2.0
session-based study work load (in a semester):
lectures
1.0
lectures
-
practices
0.0
practices
-
exercises
1.0
exercises
-
lecturer in charge
-
LECTURER SYLLABUS INFO
semester of studies
teaching lecturer / unit
language of instruction
Extended syllabus or link to Moodle or to home page
2025/2026 autumn
Dmitri Kartofelev, LT - Department of Cybernetics
English