Simple-zero and double-zero singularities of a Kaldor-Kalecki model of business cycles with delay
type: Item
instance of: scholarly article
title: Simple-zero and double-zero singularities of a Kaldor-Kalecki model of business cycles with delay
zbMATH Open document ID: 1203.91167
DOI: 10.1155/2009/923809
author: Xiaoqin P. Wu
published in: Discrete Dynamics in Nature and Society
publication date: 2010-04-26T00:00:00Z
full work available at URL: https://eudml.org/doc/230394
review text: The main aim of the paper is to study a variant of the Kaldor-Kalecki model of business cycles with delay in both the gross product and the capital stock. This work concerns the broadly discussed issue of delayed differential equations in the economic context of business cycles models. The investigated model is one of the widely recognized models of business cycles. It incorporates the ideas of Kaldor (a model of business cycles), Kalecki (the delay between an investment and a business decision) and Krawiec and Szydowski (on whose work the author bases much of his discussion), who proposed to study the ideas of Kaldor and Kalecki as one model, allowing for further modifications. The paper is organized as follows. In Section 1, an introduction is given, with particular emphasis on the economic context. The equations of Kaldor and Kalecki are written out explicitly and several references are given that discuss some of its properties. Then, a modification of Kaddar and Talibi Alaoui is presented. This modification introduces delays in both the gross product and capital stock. Kaddar and Talibi Alaoui studied the characteristic equation of the linear part of the Kalecki-Kaldor system of equations with the proposed modification (further we refer to it as the characteristic equation) at an equilibrium point and used the delay as a bifurcation parameter. In this way, they showed that a Hopf bifurcation may occur under certain conditions, when the delay passes some critical values. Their work was further extended by Wang and Wu. However, neither of the authors discussed before the issue that the characteristic equation can have a simple-zero root, a double-zero root or a simple-zero root and a pair of purely imaginary roots. The analysis of this issue is the main motivation of the described paper by Wu. Section 2 regards a detailed presentation of the distribution of eigenvalues of the linear part of the modified Kaldor-Kalecki model at an equilibrium point. The bifurcation…
reviewed by: Krzysztof Cichy
Mathematics Subject Classification ID: 91B55
Mathematics Subject Classification ID: 91B52
Mathematics Subject Classification ID: 91B64
zbMATH DE Number: 5701476
zbMATH Keywords: Kaldor-Kalecki model
zbMATH Keywords: business cycles with delay
zbMATH Keywords: bifurcation diagrams
Wikidata QID: Q58647579
MaRDI profile type: Publication
OpenAlex ID: W2025967997
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description: scientific article; zbMATH DE number 5701476