"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Dynamical systems
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
ME014
4
2+1+0
5
optional
Informatică
Teaching Staff in Charge
Lect. SERBAN Marcel Adrian, Ph.D.,  mserbanmath.ubbcluj.ro
Prof. TRIF Damian, Ph.D.,  dtrifmath.ubbcluj.ro
Lect. BUICA Adriana, Ph.D.,  abuicamath.ubbcluj.ro
Aims
The assimilation of the basic analytical and numerical methods in dynamical systems.
Content
1. Introduction: linear systems, types of nonlinearities, nonlinear behaiviours
2. Models in phase space: existence and uniqnuess, liniarization, autonomuous systems, phase portrait
3. Singular points, isocline, limit cycles, attractors, chaos
4. Harmonic analyse, oscilations, forced systems
5. Segmentar linear models
6. Stability: equilibrium points, Liapunov method, absolut stability
7. Discrete dynamical systems
8. Numerical methods for dynamical systems
References
1. COOK, P.A.: Nonlinear Dynamical Systems, Prentice-Hall, 1986.
2. TRIF, DAMIAN: Metode numerice in teoria sistemelor dinamice, Transilvania Press, 1997.
3. PETRILA, TITUS - TRIF, DAMIAN: Metode numerice si computationale in dinamica fluidelor, Ed. Digital Data Cluj, 2002.
Assessment
3 monthly tests 45% + exam 55%.