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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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    References listed on IDEAS

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    1. Bohm, Volker & Kaas, Leo, 2000. "Differential savings, factor shares, and endogenous growth cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 965-980, June.
    2. Giant-italo Bischi & Laura Gardini, 2000. "Global properties of symmetric competition models with riddling and blowout phenomena," Discrete Dynamics in Nature and Society, Hindawi, vol. 5, pages 1-12, January.
    3. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 70(1), pages 65-94.
    4. Luigi L. Pasinetti, 1962. "Rate of Profit and Income Distribution in Relation to the Rate of Economic Growth," Review of Economic Studies, Oxford University Press, vol. 29(4), pages 267-279.
    5. Ishiyama, K. & Saiki, Y., 2005. "Unstable periodic orbits and chaotic economic growth," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 33-42.
    6. Brianzoni Serena & Mammana Cristiana & Michetti Elisabetta, 2007. "Complex Dynamics in the Neoclassical Growth Model with Differential Savings and Non-Constant Labor Force Growth," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 11(3), pages 1-19, September.
    7. Szydłowski, Marek & Krawiec, Adam, 2005. "The stability problem in the Kaldor–Kalecki business cycle model," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 299-305.
    8. T. W. Swan, 1956. "ECONOMIC GROWTH and CAPITAL ACCUMULATION," The Economic Record, The Economic Society of Australia, vol. 32(2), pages 334-361, November.
    9. Bischi, Gian Italo & Gardini, Laura & Kopel, Michael, 2000. "Analysis of global bifurcations in a market share attraction model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 855-879, June.
    10. Paul A. Samuelson & Franco Modigliani, 1966. "The Pasinetti Paradox in Neoclassical and More General Models," Review of Economic Studies, Oxford University Press, vol. 33(4), pages 269-301.
    11. Becker, Robert A. & Tsyganov, Eugene N., 2002. "Ramsey Equilibrium in a Two-Sector Model with Heterogeneous Households," Journal of Economic Theory, Elsevier, vol. 105(1), pages 188-225, July.
    12. Nishimura, Kazuo, 1985. "Competitive equilibrium cycles," Journal of Economic Theory, Elsevier, vol. 35(2), pages 284-306, August.
    13. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
    14. Ken-ichi Ishiyama & Yoshitaka Saiki, 2005. "Unstable periodic orbits embedded in a chaotic economic dynamics model," Applied Economics Letters, Taylor & Francis Journals, vol. 12(12), pages 749-753.
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    Cited by:

    1. 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.
    2. 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.
    3. Agliari, Anna & Böhm, Volker & Pecora, Nicolò, 2020. "Endogenous cycles from income diversity, capital ownership, and differential savings," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. 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.

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