A Computer Program for the Numerical Analysis of Economic Cycles Within the Framework of the Dubovsky Generalized Model

TL;DR

This paper introduces a computer program that uses fractional differential equations to analyze economic cycles and crises, demonstrating how derivative orders influence the dynamics of economic models.

Contribution

It presents a novel numerical algorithm for solving Dubovsky's generalized economic model with fractional derivatives, enabling detailed analysis of economic oscillations.

Findings

Changing fractional derivative orders affects oscillation modes.

The program constructs oscillograms and phase trajectories.

Fractional derivatives influence the intensity of economic processes.

Abstract

The article proposes a computer program for calculating economic crises according to the generalized mathematical model of S.V. Dubovsky. This model is represented by a system of ordinary nonlinear differential equations with fractional derivatives in the sense of Gerasimov-Caputo with initial conditions. Furthermore, according to a numerical algorithm based on an explicit nonlocal finite-difference scheme, oscillograms and phase trajectories were constructed. It is shown that changing the orders of fractional derivatives in the model can give rise to various modes, for example, damped modes with a steady-state amplitude. It is concluded that the orders of fractional derivatives are responsible for the intensity of the process.