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Nonlinear dynamics in a business-cycle model with logistic population growth

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  • Brianzoni, Serena
  • Mammana, Cristiana
  • Michetti, Elisabetta

Abstract

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 μ). We prove the existence of complex dynamics when the elasticity of substitution between production factors drops below one (so that capital income declines) or μ increases (so that the amplitude of movements in the population growth rate increases).

Suggested Citation

  • Brianzoni, Serena & Mammana, Cristiana & Michetti, Elisabetta, 2009. "Nonlinear dynamics in a business-cycle model with logistic population growth," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 717-730.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:2:p:717-730
    DOI: 10.1016/j.chaos.2007.08.041
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    1. Brianzoni, Serena & Mammana, Cristiana & Michetti, Elisabetta, 2012. "Variable elasticity of substituition in a discrete time Solow–Swan growth model with differential saving," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 98-108.
    2. Tramontana, Fabio & Sushko, Iryna & Avrutin, Viktor, 2015. "Period adding structure in a 2D discontinuous model of economic growth," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 262-273.
    3. Fanti, Luciano & Gori, Luca & Mammana, Cristiana & Michetti, Elisabetta, 2013. "The dynamics of a Bertrand duopoly with differentiated products: Synchronization, intermittency and global dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 73-86.
    4. Michetti, Elisabetta, 2015. "Complex attractors and basins in a growth model with nonconcave production function and logistic population growth rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 215-232.
    5. Luciano Fanti & Luca Gori, 2012. "Public Expenditure on Health and Private Old-Age Insurance in an OLG Growth Model with Endogenous Fertility: Chaotic Dynamics Under Perfect Foresight," Computational Economics, Springer;Society for Computational Economics, vol. 40(4), pages 333-353, December.
    6. Grassetti, Francesca & Mammana, Cristiana & Michetti, Elisabetta, 2018. "Substitutability between production factors and growth. An analysis using VES production functions," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 53-62.
    7. Francesca Grassetti & Cristiana Mammana & Elisabetta Michetti, 2018. "Poverty trap, boom and bust periods and growth. A nonlinear model for non-developed and developing countries," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 145-162, November.
    8. Serena Brianzoni & Cristiana Mammana & Elisabetta Michetti, 2012. "Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function," Working Papers 70-2012, Macerata University, Department of Finance and Economic Sciences, revised Sep 2015.
    9. Agliari, Anna & Böhm, Volker & Pecora, Nicolò, 2020. "Endogenous cycles from income diversity, capital ownership, and differential savings," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).

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