IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2013y2013i1n689372.html

Stability Switches and Hopf Bifurcation in a Kaleckian Model of Business Cycle

Author

Listed:
  • Luca Vincenzo Ballestra
  • Luca Guerrini
  • Graziella Pacelli

Abstract

This paper considers a Kaleckian type model of business cycle based on a nonlinear delay differential equation, whose associated characteristic equation is a transcendental equation with delay dependent coefficients. Using the conventional analysis introduced by Beretta and Kuang (2002), we show that the unique equilibrium can be destabilized through a Hopf bifurcation and stability switches may occur. Then some properties of Hopf bifurcation such as direction, stability, and period are determined by the normal form theory and the center manifold theorem.

Suggested Citation

  • Luca Vincenzo Ballestra & Luca Guerrini & Graziella Pacelli, 2013. "Stability Switches and Hopf Bifurcation in a Kaleckian Model of Business Cycle," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:689372
    DOI: 10.1155/2013/689372
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/689372
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/689372?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Paul Zak, 1999. "Kaleckian Lags in General Equilibrium," Review of Political Economy, Taylor & Francis Journals, vol. 11(3), pages 321-330.
    2. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
    3. Matsumoto, Akio & Szidarovszky, Ferenc, 2011. "Delay differential neoclassical growth model," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 272-289, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Luca Guerrini & Mauro Sodini, 2013. "Nonlinear Dynamics in the Solow Model with Bounded Population Growth and Time‐to‐Build Technology," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gori, Luca & Guerrini, Luca & Sodini, Mauro, 2015. "A continuous time Cournot duopoly with delays," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 166-177.
    2. Franke, Reiner, 2018. "Reviving Kalecki’s business cycle model in a growth context," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 157-171.
    3. Luca Guerrini, 2012. "Constant population growth rate and time to build: the Solow model case," Economics Bulletin, AccessEcon, vol. 32(4), pages 3260-3265.
    4. Luca Guerrini & Mauro Sodini, 2013. "Nonlinear Dynamics in the Solow Model with Bounded Population Growth and Time‐to‐Build Technology," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Ishida, Junichiro & Yokoo, Masanori, 2004. "Threshold nonlinearities and asymmetric endogenous business cycles," Journal of Economic Behavior & Organization, Elsevier, vol. 54(2), pages 175-189, June.
    6. Matsumoto, Akio & Szidarovszky, Ferenc, 2023. "Delay Solow Model with a Normalized CES Production Function," Journal of Economic Behavior & Organization, Elsevier, vol. 213(C), pages 305-323.
    7. Massimiliano Ferrara & Luca Guerrini & Giovanni Molica Bisci, 2013. "Center Manifold Reduction and Perturbation Method in a Delayed Model with a Mound‐Shaped Cobb‐Douglas Production Function," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. Yüksel, Mustafa Kerem, 2011. "Capital dependent population growth induces cycles," Chaos, Solitons & Fractals, Elsevier, vol. 44(9), pages 759-763.
    9. Matteo Bizzarri & Marco Pangallo & Francisco Queirós, 2025. "Production Networks, Time to Build and Endogenous Oscillations," CSEF Working Papers 764, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    10. Ulrich Brandt-Pollmann & Ralph Winkler & Sebastian Sager & Ulf Moslener & Johannes Schlöder, 2008. "Numerical Solution of Optimal Control Problems with Constant Control Delays," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 181-206, March.
    11. Ghassan Dibeh, 2001. "Time Delays and Business Cycles: Hilferding's model revisited," Review of Political Economy, Taylor & Francis Journals, vol. 13(3), pages 329-341.
    12. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Working Papers hal-03145949, HAL.
    13. Kitagawa, Akiomi & Shibata, Akihisa, 2001. "Long gestation in an overlapping generations economy: endogenous cycles and indeterminacy of equilibria," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 99-127, February.
    14. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics.
    15. Heinzel, Christoph & Winkler, Ralph, 2006. "Gradual versus structural technological change in the transition to a low-emission energy industry: How time-to-build and differing social and individual discount rates influence environmental and technology policies," Dresden Discussion Paper Series in Economics 09/06, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    16. Shaikhet, Leonid, 2023. "Stability of equilibria of exponential type system of three differential equations under stochastic perturbations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 105-117.
    17. Richard Hartl & Peter Kort, 2010. "Delay in finite time capital accumulation," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(4), pages 465-475, December.
    18. Olivia BUNDAU & Mihaela NEAMTU, 2009. "The Analysis of an Economic Growth Model with Tax Evasion and Delay," Timisoara Journal of Economics, West University of Timisoara, Romania, Faculty of Economics and Business Administration, vol. 2(1(5)), pages 13-18.
    19. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    20. Ralph Winkler, 2008. "Optimal control of pollutants with delayed stock accumulation," CER-ETH Economics working paper series 08/91, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:689372. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.