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

Code	Subject	
MME0005	Economics Dynamics	

Section	Sem.	Hours: C+S+L	Category	Type	
Mathematics - in Romanian	5	2+1+0	speciality	optional	
Mathematics-Computer Science - in Romanian	5	2+1+0	speciality	optional	
Applied Mathematics	5	2+1+0	speciality	compulsory	

Teaching Staff in Charge	Asist. ILEA Veronica Ana, vdarzu@math.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

Bibliography	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:

60% two writtent test during the semester;
30% one written report at the end of semester;
10% home works.