Numerical Modeling of Kondratyev's Long Waves Taking into Account Heredity

TL;DR

This paper introduces a fractional calculus-based mathematical model for economic cycles that incorporates heredity effects and investment dynamics, revealing potential for both regular and chaotic behaviors.

Contribution

It generalizes Dubovsky's model by including heredity and investment functions using Gerasimov-Caputo derivatives, analyzed through numerical methods.

Findings

Model exhibits both regular and chaotic regimes

Incorporates heredity effects into economic cycle modeling

Uses fractional derivatives for more accurate dynamics

Abstract

The paper proposes a new mathematical model of economic cycles and crises, which generalizes the well-known model of Dubovsky S.V. The novelty of the proposed model lies in taking into account the effect of heredity (memory), as well as the introduction of harmonic functions responsible for the arrival of investments in fixed assets and new management technologies in innovation. The mathematical description is given using the Gerasimov-Caputo fractional derivatives, which are studied within the framework of the theory of fractional calculus. The mathematical model was investigated using the numerical method of Adams-Bashforth-Moulton (ABM), phase trajectories were constructed. It is shown that the proposed mathematical model can have both regular and chaotic regimes.