Dynamical Systems

Contents:
The goal of the course is to develop the quantitative and qualitative theory of differential and difference equations and to look at relevant examples which illustrate this theory.

 

Section 1: Ordinary Differential Equations
a.          First – order differential equations, Domar growth model, Dynamics of market prices

b.         Nonlinear differential equations: The qualitative approach. Solow growth model

c.          Second- order linear differential equations. A market model with price expectations. The interaction of inflation and unemployment

 

Section 2: Difference Equations
a.         First – order linear difference equations, the dynamic stability of equilibrium, the cobweb model, a market model with inventory

b.         Nonlinear difference equations- the qualitative approach.

c.         Second- order linear difference equations, Samuelson multiplier- acceleration interaction model, inflation and unemployment in discrete time

 

Section 3: Systems of Differential and Difference Equations
a.      Linear systems of differential and difference equations. The inflation – unemployment model

b.     Nonlinear system: Two – variable phase diagrams, linearization of a nonlinear differential- equation system.

 

Section 4: Optimal Control Theory
a.         Potryagin’s Maximum Principle. Alternative of terminal conditions

b.        Autonomous problem

c.         Economic applications

 

Bibliography:

·       G. Sarafopoulos, N. Mylonas, Mathematical Economics (in Greek), Ed. Tziolas,2019 (Primary textbook)

·       E. Dowling, Introduction to Mathematical Economics, McGraw – Hill (Shaum’s series), 2001

·       M. Hoy et al. Mathematics for Economists, Addison Wesley, 2001

·       C. Simon – L. Blume, Mathematics for Economists Norton Co.,2004