Course: Nonlinear Dynamics and Chaos

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Course title Nonlinear Dynamics and Chaos
Course code KME/NDY
Organizational form of instruction Lecture
Level of course Bachelor
Year of study 3
Semester Summer
Number of ECTS credits 3
Language of instruction Czech
Status of course Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Rosenberg Josef, Prof. Ing. DrSc.
Course content
1.Overview of dynamical oscillators - motivation 2.Basic terms from the nonlinear dynamical systems theory, continuous and discrete dynamical systems 3.Fixed points and attractors in autonomous systems - ecological systems 4.Limit cycles in autonomous systems - bifurcation types, bifurcation in chemical oscillator, quasiperiodic solution 5.Periodic and chaotic attractors of excited oscillators - Poincare's notation 6.Van der Pol oscillator, Birkhoff-Shaw chaotic attractor 7.Duffing oscillator 8.Stability and bifurcation of iterative mappings. Chaos of iterative mappings, logical mapping, Smale horseshoe 9.Types of chaos transition, period doubling, intermitance, quasiperiodic way, crisis 10.Lorenz system 11.Rossler band 12.Chosed applications

Learning activities and teaching methods
Lecture with visual aids
  • Preparation for an examination (30-60) - 60 hours per semester
  • Contact hours - 39 hours per semester
prerequisite
professional knowledge
The student knows - theoretical mechanics of discrete mechanical systems - matrix calculus - linear oscillation theory
learning outcomes
The student - is familiar with the theory of dynamical systems and their application to concrete problems - apply acquired knowledge to analyze concrete problems - knows to find the approximations of simpler nonlinear problems solution
teaching methods
Lecture with visual aids
assessment methods
Oral exam
Recommended literature
  • Kapitaniak, Tomasz. Chaos for engineers : theory, applications, and control. [1st ed.]. Berlin : Springer, 1998. ISBN 3-540-63515-7.
  • Scheck,F. Mechanik - Von den Newtonschen Gesetzen zum deterministischen Chaos. Springer - Verlag, 1992.
  • Thompson, J. M. T.; Stewart, H. B. Nonlinear dynamics and chaos. 2nd ed. Chichester : John Wiley & Sons, 2002. ISBN 0-471-87684-4.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 3 Summer
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 3 Summer