Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate

SUBJECT

Code
Subject
MME0005 Economics Dynamics
Section
Semester
Hours: C+S+L
Category
Type
Mathematics - in Romanian
5
2+1+0
speciality
optional
Applied Mathematics
5
2+2+0
speciality
compulsory
Teaching Staff in Charge
Prof. PETRUSEL Adrian Olimpiu, Ph.D.,  petruselmath.ubbcluj.ro
Aims
The main goal of the course is to provide students with some basic concepts and tools from the theory of discrete and continuous dynamical systems, to develop the capacity to analyse and to synthesize the dynamic behaviour of the models generated by some problems from finance and from economy.
Content
1. Continuous Dynamical Systems (The concept of dynamical system, Examples: dynamical systems generated topological isomorphisms, dynamical systems generated by differential equations);
a) dynamical systems generated by differential equations: basic concepts and tools;
b) fixed points, periodic points, attractors, limit sets in R and in the plane;
c) stability for equilibrium solutions (sufficient conditions for asymptotic stability), trajectories, phase portrait, in R and in the plane;
2. Discrete Dynamical Systems (classification)
a) discrete dynamical systems of firest order;
b) discrete dynamical systems of second order;
c) stability for discrete dynamical systems, the linear and the nonlinear case;
3. Numerical Methods for dynamical systems
4. Economic Dynamics
a) supply and demand dynamics
b) Keynesian Dynamics
c) IS-LM dynamics
d) the dynamics of inflation and unemployment

References
1. R. Shone, An Introduction to Economics Dynamics, Cambridge University Press, 2001.
2. I.A. Rus, Ecuatii diferentiale, ecuatii integrale si sisteme dinamice, Transilvania Press, Cluj-Napoca, 1996.
3. S. Elaydi: An Introduction to Difference Equations, Sprimger-Verlag, 2003.
4. B. Hasselblatt, A. Katok: A First Course in Dynamics, Cambridge Univ. Press, 2003.
5. W.A. Brock, A.G. Malliaris, Differential Equations, Stability and Chaos in Dynamic Economics, North-Holland,Amsterdam, 1989.
6. R. Shone: Economic Dynamics, Cambridge University Press, 2004.
7. L. Perko: Differential Equations and Dynamical Systems, Springer Verlag, 1996.

Assessment
The final mark is composed by:

50% two writtent test during the semester;
25% one written report at the end of semester;
25% home works.

Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject