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Zbl 1197.91145
Brianzoni, Serena; Mammana, Cristiana; Michetti, Elisabetta
Nonlinear dynamics in a business-cycle model with logistic population growth.
(English)
[J] Chaos Solitons Fractals 40, No. 2, 717-730 (2009). ISSN 0960-0779

Summary: We consider a discrete-time growth model of the Solow type where workers and shareholders have different but constant saving rates and the population growth dynamics is described by the logistic equation able to exhibit complicated dynamics. We show conditions for the resulting system having a compact global attractor and we describe its structure. We also perform a mainly numerical analysis using the critical lines method able to describe the strange attractor and the absorbing area, in order to show how cyclical or complex fluctuations may be produced in a business-cycle model. We study the dynamic behaviour of the model under different ranges of the main parameters, i.e. the elasticity of substitution between the two production factors and the one in the logistic equation (namely $\mu$). We prove the existence of complex dynamics when the elasticity of substitution between production factors drops below one (so that capital income declines) or $\mu$ increases (so that the amplitude of movements in the population growth rate increases). \par Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.
MSC 2000:
*91B62 Dynamic economic models etc.
37N40 Dynamical systems in optimization and economics
37D45 Strange attractors, chaotic dynamics

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