Numerical Analysis of Two Coupled Kaldor-Kalecki Models with Delay

Abstract

This paper is concerned with two coupled Kaldor-Kalecki models of business cycles with delays in both the gross product and the capital stock. We consider two types of investment functions that lead to different behavior of the system. We introduce the model with unidirectional coupling to investigate the influence of a global economy (like the European Union) on a local economy (like Poland). We present detailed results of numerical analysis.

Bifurcations in an economic growth model with a distributed time delay transformed to ODE

“…While mostly the discrete delay was investigated, some Kaldor-Kalecki models with distributed delays were also proposed. The Kaldor-Kalecki models with fixed delay include both models with one delay and two delays [28][29][30][31][32].…”

Numerical Analysis of Modified Kaldor-Kalecki Model with Couplings and Delays

“…The remaining two systems: (y 3 , y 4 ) and (y 5 , y 6 ) represent "local" economies, say, Poland and Germany. Later on we will justify such a choice by a proper adjustment of relevant parameters.Following our previous arguments [8] we construct a set of ten equations describing five mutually interacting economies with delays and both unidirectional and bidirectional couplings:−s 5 (y 9 (t) − y 1 (t)) + s 6 (y 7 (t) − y 1 (t)),−y 3 (t)) + s 10 (y 7 (t) − y 3 (t)) − s 12 (y 5 (t) − y 3 (t)), y 5 = α 3 (F 3 (t) − δ 3 y 6 (t) − γ 3 y 5 (t)),−y 5 (t)) + s 9 (y 7 (t) − y 5 (t)) − s 13 (y 3 (t) − y 5 (t)),ẏ 7 = α 4 (F 4 (t) − δ 4 y 8 (t) − γ 4 y 7 (t)),−y 7 (t)) − s 11 (y 1 (t) − y 7 (t)), y 9 = α 5 (F 5 (t) − δ 5 y 10 (t) − γ 5 y 9 (t)),−y 9 (t)) + s 7 (y 7 (t) − y 9 (t)).Here F i (t) (i = 1, . .…”

“…It seems that especially fruitful are various versions and generalizations of Kaldor-Kalecki models [4][5][6][7]. Quite recently we have proposed another generalization that takes into account the interactions between two economies [8]. Such interactions are inevitable in real life situations and in the present paper we develop a more realistic model of three "global" and two "local" economies mutually interacting in a way resembling actual economical influences and relationships between countries on the global market.…”

“…Following our previous arguments [8] we construct a set of ten equations describing five mutually interacting economies with delays and both unidirectional and bidirectional couplings:…”