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, BirkhoffShaw 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 (3060)
 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 3540635157.

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 0471876844.
