STABILITY ANALYSIS OF THE PALOMBA MODEL IN ECONOMY BY FRACTIONAL-ORDER DIFFERENTIAL EQUATIONS WITH MULTI-ORDERS

Abstract

Author(s): Bahatdin DA?BA?I, Dervi? BOZTOSUN

In economics, a model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. In this sense, the economic model is a simplified, usually mathematical, framework designed to illustrate complex processes. Lotka-Volterra model is widely used in the economy and is up-to-date. The author famous for introducing the Lotka-Volterra dynamics in economics is Goodwin (1967). But, as indicated by Massimo di Mateo in 1988, the economist Giuseppe Palomba had used these equations in a book published in 1939. Palomba proposed the mathematical model formed by ordinary differential equation (ODE) considered an economy where there are only two types of goods: consumption goods, such as clothing and food, and capital goods, such as buildings and machinery. In this study, the Palomba model in economy was expressed by the fractional-order differential equations (FDE) with multiple order. Stability analysis was made by finding the equilibrium points of the model. In addition, the analysis of the model was graphically supported. According to the results of the analysis, it was showed the stability of the equilibrium point where these two types of goods existed positively.

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