Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Nonlinear dynamics, chaos and fractals-application in engineering (17.DOM82)

Type of studies	Title
Doctoral Academic Studies	Mathematics in Engineering (Year: 1, Semester: Winter)
Doctoral Academic Studies	Mathematics in Engineering (Year: 2, Semester: Winter)

General information:

Category	Scientific-professional
Scientific or art field	Physics
ECTS	10

Deeper understanding of nonlinear processes doing homework exercises with possibility of using computers. Understanding of nonlinear problems in Technical applications.

Students are capable to solve nonlinear problems in technique.

1. ONE-dimensional or first-order systems; A geometric way of thinking. Intepreting a differential equation as a vector field. 2. Fixed points and stability of system (example: population growth). 3. Linear stability analysis. 4. Bifurcations; Transcritical Bifurcations (example: LASER threshold). 5. Two dimensional linear systems classification of fixed points. 6. Phase plane and phase portraits. 7. Limit cycles; Poincare-Bendixon theorem. 8. Conservative systems; Reversible systems.

Lectures. Consultations. Theoretical part of the material is being presented on the lectures, accompanied by appropriate characteristic examples of the application of physical principles in mathematics and technique.

Authors	Title	Year	Publisher	Language
L. Cesani	Asymptotic Behavior and Stability Problems in Ordinary Differential Equations	1963	Academic, New York	English
D.K. Arrowsmith and C.M. Place	An Introduction to Dynamical Systems	1990	Camridge University Press	English
Steven H. Strogatz	Nonlinear Dynamics and Chaos	1994	Perseus Books Publishing	English