From bi-stability to chaotic oscillations in a macroeconomic model
type: Item
instance of: scholarly article
title: From bi-stability to chaotic oscillations in a macroeconomic model
zbMATH Open document ID: 1032.91093
DOI: 10.1016/S0960-0779(00)00055-2
author: Roberto Dieci
author: Gian-Italo Bischi
author: Laura Gardini
published in: Chaos, Solitons and Fractals
publication date: 2003-03-19T00:00:00Z
review text: A discrete-time economic model is considered where the savings are proportional to income and the investment demand depends on the difference between the current income and its exogenously assumed equilibrium level, through a nonlinear \(S\)-shaped increasing function. The model can be ultimately reduced to a two-dimensional discrete dynamical system in income and capital, whose time evolution is ``driven'' by a family of two-dimensional maps of triangular type. These particular two-dimensional maps have the peculiarity that one of their components appears to be uncoupled from the other, i.e., an independent one-dimensional map. The structure of such maps allows to understand completely the forward dynamics, i.e., the asymptotic dynamic behavior, starting from the properties of the associated one-dimensional map. The equilibrium points of the map are determined, and the influence of the main parameters on the local stability of the equilibria is studied. More important, the paper analyzes how changes in the parameters' values modify both the asymptotic dynamics of the system and the structure of the basins of the different and often coexisting attractors in the phase-plane. Finally, a particular ``global'' bifurcation is illustrated, occurring for sufficiently high values of the firms' adjustment parameter and causing the switching from a situation of bi-stability to a regime characterized by wide chaotic oscillations of income and capital around their exogenously assumed eguilibrium levels.
Mathematics Subject Classification ID: 91B62
Mathematics Subject Classification ID: 37N40
Mathematics Subject Classification ID: 91B64
zbMATH DE Number: 1884587
zbMATH Keywords: discrete-time economic model
zbMATH Keywords: forward dynamics
zbMATH Keywords: equilibrium points
zbMATH Keywords: local stability
zbMATH Keywords: bifurcation
reviewed by: Marian Matłoka
MaRDI profile type: Publication
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Wikidata QID: Q127354007
description: scientific article; zbMATH DE number 1884587