Differential Equations and Dynamical Systems

Course Description

Legendre, Chebyshev and Hermit functions and differential equations. Qualitative analysis of differential equations presented on the model of Euler and Bessel differential equations. Oscillations and method of Riccati differential equation. Explicit, numerical and asymptotic methods for differential equations and systems. Models and applications: oscillators, pendulums, nonlinear electronic circuits. Robustness of discrete and continuous systems, Lyapunov stability and bifurcations. Saddle-node bifurcation, Hopf, Hopf-Takens, Bogdanov-Takens bifurcations. Chaos and criteria for chaos in systems. Lorenz system.

Study Programmes

Postgraduate doctoral study programme

Literature

A. C. King, J. Billingham, S. R. Otto (2003.), Differential Equations, Cambridge University Press
Lawrence Perko (2008.), Differential Equations and Dynamical Systems, Springer Science & Business Media
Luka Korkut, Vesna Županović (2009.), Diferencijalne jednadžbe i teorije stabilnosti, Element, Zagreb
Steven H. Strogatz (2014.), Nonlinear Dynamics and Chaos, Westview Press
Mervan Pašić (2013.), Fite-Wintner-Leighton type oscillation criteria for second-order differential equations with nonlinear damping, Abstract and Applied Analysis
Mervan Pašić (2007.), Rectifiable and unrectifiable oscillations for a class of second-order linear differential equations of Euler type, Journal of Mathematical Analysis and Application

For students

General

ID 154703
  Winter semester
6 ECTS
L0 English Level