Stability of solutions of differential equations and its application in economic models
|Author:||Bc. Filip Ravinger|
|Year:||2005 - summer|
|Leaders:|| doc. RNDr. Miroslav Zelený Ph.D.
|Work type:|| Bachelors
|Awards and prizes:|
|Abstract:||Differential equations represent one of possible methods for modelling dynamic systems. This paper seeks to illustrate how the apparatus of differential equations can be applied in economic modelling and to emphasise their importance in description of real-world processes. Qualitative analysis of the solutions of systems of differential equations is primarily focused on. The central notion of the paper is the notion of stability of solutions, which is interpreted in economic application as stability of given system of simultaneously acting economic factors.
The first chapter examines in detail the mathematical tools that are used to accurately construct the dynamic model. The
grounds of the theory of systems of differential equations is explained. This knowledge and the particular techniques are then utilised in the second chapter, where the model of Walrasian competitive equilibrium is studied. The main issue is the question of stability of the equilibrium price adjustment process. Mathematically correct exposition is one of the aims of the paper.