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Multiple attractors and global bifurcations in a Kaldor-type business cycle model

Author

Listed:
  • Giorgio Rodano

    (Dipartimento di Teoria Economica e Metodi Quantitativi, Universit, "La Sapienza", Roma, Italy)

  • Gian Italo Bischi

    (Istituto di Scienze Economiche, University of Urbino, 61029 Urbino, Italy)

  • Enrico Saltari

    (Istituto di Scienze Economiche, University of Urbino, 61029 Urbino, Italy)

  • Roberto Dieci

    (Dipartimento di Economia, University of Parma, via Kennedy 6B, 43100 Parma, Italy)

Abstract

We consider a Kaldor-type discrete-time nonlinear business cycle model in income and capital, where investment is assumed to depend both on the difference between normal and current levels of capital stock, and on the difference between the current income and its normal level, through a nonlinear S-shaped increasing function. As usual in Kaldor business cycle models, one or three steady states exist, and the standard analysis of the local stability and bifurcations suggests that endogenous oscillations occur in the presence of only one unstable equilibrium, whereas the coexistence of three equilibria is characterized by bi-stability, the central equilibrium being on the boundary which separates the basins of the two stable ones. However, a deeper analysis of the global dynamic properties of the model in the parameter ranges where three steady states exist, reveals the existence of an attracting limit cycle surrounding the three steady states, leading to a situation of multistability, with a rich and complex dynamic structure.

Suggested Citation

  • Giorgio Rodano & Gian Italo Bischi & Enrico Saltari & Roberto Dieci, 2001. "Multiple attractors and global bifurcations in a Kaldor-type business cycle model," Journal of Evolutionary Economics, Springer, vol. 11(5), pages 527-554.
    • Handle: RePEc:spr:joevec:v:11:y:2001:i:5:p:527-554
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    Cited by:

    1. Fausto Cavalli & Ahmad Naimzada & Nicol`o Pecora & Marina Pireddu, 2018. "Agents' beliefs and economic regimes polarization in interacting markets," Papers 1805.00387, arXiv.org.
    2. Fausto Cavalli & Ahmad Naimzada & Marina Pireddu, 2015. "Effects of Size, Composition, and Evolutionary Pressure in Heterogeneous Cournot Oligopolies with Best Response Decisional Mechanisms," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-17, May.
    3. Lixiao Hao & Vasilios I. Manousiouthakis, 2021. "Sustainability over sets and the business cycle," SN Business & Economics, Springer, vol. 1(6), pages 1-26, June.
    4. Pasquale Commendatore & Carlo Panico & Antonio Pinto, 2011. "The Influence Of Different Forms Of Government Spending On Distribution And Growth," Metroeconomica, Wiley Blackwell, vol. 62(1), pages 1-23, February.
    5. Irina Bashkirtseva & Alexander Pisarchik & Lev Ryashko & Tatyana Ryazanova, 2016. "Excitability And Complex Mixed-Mode Oscillations In Stochastic Business Cycle Model," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 19(01n02), pages 1-16, February.
    6. Dobrescu, Loretti I. & Opris, Dumitru, 2009. "Neimark–Sacker bifurcation for the discrete-delay Kaldor model," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2462-2468.
    7. Roman Binter & Lukáš Vácha, 2005. "Local Stability and Bifurcations in Kaldor Model [Lokální stabilita a bifurkace v Kaldorově modelu]," Acta Oeconomica Pragensia, Prague University of Economics and Business, vol. 2005(1), pages 10-20.
    8. Giuseppe Orlando & Fabio Della Rossa, 2019. "An Empirical Test on Harrod’s Open Economy Dynamics," Mathematics, MDPI, vol. 7(6), pages 1-13, June.
    9. Irina Bashkirtseva & Davide Radi & Lev Ryashko & Tatyana Ryazanova, 2018. "On the Stochastic Sensitivity and Noise-Induced Transitions of a Kaldor-Type Business Cycle Model," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 699-718, March.
    10. Commendatore, Pasquale & Panico, Carlo & Pinto, Antonio, 2007. "Composition of public expenditure, effective demand, distribution and growth," MPRA Paper 9085, University Library of Munich, Germany.
    11. Orlando Gomes, 2007. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing, vol. 33(6), pages 437-468, January.
    12. Velasco Morente, Francisco & Nadal Morales, Purificación & González Abril, Luis & Ortega Ramírez, Juan Antonio, 2009. "Bifurcaciones de codimensión 2 en un modelo dinámico del mercado potencial y actual: aplicación al mercado cervecero español = Bifurcations of Codimension 2 in a Dynamical Model of Current and Potenti," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 7(1), pages 77-94, June.
    13. Orlando Gomes, 2006. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing, vol. 33(6), pages 437-468, November.
    14. Bischi, Gian-Italo & Gallegati, Mauro & Gardini, Laura & Leombruni, Roberto & Palestrini, Antonio, 2006. "Herd Behavior And Nonfundamental Asset Price Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 10(4), pages 502-528, September.
    15. Loretti I. Dobrescu & Dumitru Opris, 2008. "Hopf bifurcation for the discrete - delay Kaldor - Kalecki model," "Marco Fanno" Working Papers 0067, Dipartimento di Scienze Economiche "Marco Fanno".
    16. Agliari, Anna & Dieci, Roberto & Gardini, Laura, 2007. "Homoclinic tangles in a Kaldor-like business cycle model," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 324-347, March.
    17. Westerhoff Frank H., 2006. "Nonlinear Expectation Formation, Endogenous Business Cycles and Stylized Facts," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(4), pages 1-17, December.

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