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Van Der Pol's Equation and an Economic Model of Cycles


  • Miloslav Vošvrda


The Van der Pol's equation (VdPe) with an appropriate feedback is applied on construction of a model of economic cycles. The model exhibits the ability of the savings and investments to give output in a limit cycle by bifurcation. According to the life cycle hypothesis, the households will have a constant, or will continuously increase, the marginal propensity to saving. The saving deviation is accelerated in relation with the gap between the GDP and its potential value of the GDP, i.e., GDP is measured by full employment of the industrial capacity. A behavior of VdPe is analysed in dependence on different levels of capital/output rotio respectivelly. The behavior of the economic model of cycles is analyzed under the three conditions: Potential output will be considered as fixed constant, Potential output will be considered with constant rote of growth, Potential output will be considered with increasing rote of growth.

Suggested Citation

  • Miloslav Vošvrda, 1999. "Van Der Pol's Equation and an Economic Model of Cycles," Bulletin of the Czech Econometric Society, The Czech Econometric Society, vol. 6(10).
  • Handle: RePEc:czx:journl:v:6:y:1999:i:10:id:74

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    References listed on IDEAS

    1. Dirk Tasche, 2004. "The single risk factor approach to capital charges in case of correlated loss given default rates," Papers cond-mat/0402390,, revised Feb 2004.
    2. Konstantin Belyaev & Aelita Belyaeva & Tomas Konecny & Jakub Seidler & Martin Vojtek, 2012. "Macroeconomic Factors as Drivers of LGD Prediction: Empirical Evidence from the Czech Republic," Working Papers 2012/12, Czech National Bank, Research Department.
    3. Acharya, Viral V. & Bharath, Sreedhar T. & Srinivasan, Anand, 2007. "Does industry-wide distress affect defaulted firms? Evidence from creditor recoveries," Journal of Financial Economics, Elsevier, vol. 85(3), pages 787-821, September.
    4. Jiri Witzany, 2011. "A Two Factor Model for PD and LGD Correlation," Bulletin of the Czech Econometric Society, The Czech Econometric Society, vol. 18(28).
    5. Jon Frye, 2000. "Depressing recoveries," Emerging Issues, Federal Reserve Bank of Chicago, issue Oct.
    6. Stefano Caselli & Stefano Gatti & Francesca Querci, 2008. "The Sensitivity of the Loss Given Default Rate to Systematic Risk: New Empirical Evidence on Bank Loans," Journal of Financial Services Research, Springer;Western Finance Association, vol. 34(1), pages 1-34, August.
    7. Seidler, Jakub & Horvath, Roman & Jakubík, Petr, 2009. "Estimating expected loss given default in an emerging market: the case of Czech Republic," Journal of Financial Transformation, Capco Institute, vol. 27, pages 103-107.
    8. De Graeve, F. & Kick, T. & Koetter, M., 2008. "Monetary policy and financial (in)stability: An integrated micro-macro approach," Journal of Financial Stability, Elsevier, vol. 4(3), pages 205-231, September.
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    More about this item


    A model of economic cycles; the life cycle hypothesis; the chaotic 3D system; the bifurcation; the limit cycle;

    JEL classification:

    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles


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