Faculty of Technical Sciences

Subject: Chaos in Dynamical Systems (17.DM405)

Native organizations units: Chair of Machine Elements, Machine and Mechanism Theory and Mechanical Engineering in Agriculture
General information:
 
Category Scientific-professional
Scientific or art field Mechanics
Interdisciplinary Yes
ECTS 10
Educational goal:

Development of abstract thinking and mastering methods of chaos testing in dynamic systems.

Educational outcome:

Ability to recognize and analyse chaotic movements of mechanic systems.

Course content:

Qualitative dynamics. Vector field as a dynamic system. Balance position and their stability. Attractors. Poincare conjecture. Bifurcation of periodic orbits. Chaos in deterministic systems. Criterion for chaos existing. Melnikov criterion. Numerical method for chaotic movement analysis. Qualitative measures of deterministic chaos. Ljapunov characteristic exponent. Strange attractors. Examples of chaos: Van der Pol`s oscillator, Duffing equation, Lorenz equations.

Teaching methods:

Lectures, study research work and consultations. The lectures provide a theoretical part of the material using modern equipment and information and communication technologies. Through lectures, a student acquires and mastered contemporary scientific knowledge, scientific methods and procedures that enable him to become independent research work. In addition to lectures, consultations are also held regularly. Study research work includes all forms of teaching that are in the function of directly training a student for research, writing scientific papers and making a doctoral dissertation. Study research work includes active monitoring of primary scientific sources, organization and execution of numerical simulations and experimental research.

Literature:
Authors Title Year Publisher Language
S. Wiggins Global Bifurcations and Chaos 1988 Springer-Verlag, NY English
Broer, H. Takens, F. Dynamical Systems and Chaos 2011 Springer English
J. Guckenheimer and P. Holmes Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields 1983 Springer-Verlag NY English
Cveticanin, L. Dynamics of Bodies with Time-Variable Mass 2015 Springer English
J.M.T. Thompson and H.B. Stewart Nonlinear Dynamics and Chaos 1986 John Wiley and Sons, NY English
Knowledge evaluation:
Course activity Pre-examination Obligations Number of points
Project Yes Yes 50.00
Oral part of the exam No Yes 50.00
Lecturers:
API Image

prof. dr Zuković Miodrag

Full Professor

Study research work
API Image

prof. dr Zuković Miodrag

Full Professor

Lectures

Faculty of Technical Sciences

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© 2024. Faculty of Technical Sciences.