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Discrete Dynamics in Nature and Society
Volume 2009, Article ID 923809, 29 pages
http://dx.doi.org/10.1155/2009/923809
Research Article

Simple-Zero and Double-Zero Singularities of a Kaldor-Kalecki Model of Business Cycles with Delay

Department of Mathematics, Computer & Information Sciences, Mississippi Valley State University, Itta Bena, MS 38941, USA

Received 12 August 2009; Accepted 2 November 2009

Academic Editor: Xue-Zhong He

Copyright © 2009 Xiaoqin P. Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. N. Kaldor, “A model of the trade cycle,” The Economic Journal, vol. 40, pp. 78–92, 1940. View at Google Scholar
  2. N. Kalecki, “A macrodynamic theory of business cycles,” Econometrica, vol. 3, pp. 327–344, 1935. View at Google Scholar
  3. A. Krawiec and M. Szydłowski, “The Kaldor-Kalecki business cycle model,” Annals of Operations Research, vol. 89, pp. 89–100, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. M. Szydłowski and A. Krawiec, “The Kaldor-Kalecki model of business cycle as a two-dimensional dynamical system,” Journal of Nonlinear Mathematical Physics, vol. 8, supplement, pp. 266–271, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. Krawiec and M. Szydłowski, “The Hopf bifurcation in the Kaldor-Kalecki model,” in Computation in Economics, Finance and Engineering: Economics Systems, S. Holly and S. Greenblatt, Eds., pp. 391–396, Elsevier, Amsterdam, The Netherlands, 2000. View at Google Scholar
  6. A. Krawiec and M. Szydłowski, “On nonlinear mechanics of business cycle model,” Regular & Chaotic Dynamics, vol. 6, no. 1, pp. 101–118, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  7. M. Szydłowski and A. Krawiec, “The stability problem in the Kaldor-Kalecki business cycle model,” Chaos, Solitons & Fractals, vol. 25, no. 2, pp. 299–305, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. Szydłowski, A. Krawiec, and J. Tobola, “Nonlinear oscillations in business cycle model with time lags,” Chaos, Solitons & Fractals, vol. 12, no. 3, pp. 505–517, 2001. View at Publisher · View at Google Scholar
  9. Y. Takeuchi and T. Yamamura, “Stability analysis of the Kaldor model with time delays: monetary policy and government budget constraint,” Nonlinear Analysis: Real World Applications, vol. 5, no. 2, pp. 277–308, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. X. P. Wu and L. Wang, “Multi-parameter bifurcations of the Kaldor-Kalecki model of business cycles with delay,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 869–887, 2010. View at Publisher · View at Google Scholar
  11. C. Zhang and J. Wei, “Stability and bifurcation analysis in a kind of business cycle model with delay,” Chaos, Solitons & Fractals, vol. 22, no. 4, pp. 883–896, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. W. W. Chang and D. J. Smith, “The existence and persistence of cycles in a nonlinear model: Kaldor's 1940 model re-examined,” The Review of Economic Studies, vol. 38, pp. 37–44, 1971. View at Google Scholar
  13. J. Grasman and J. J. Wentzel, “Co-existence of a limit cycle and an equilibrium in Kaldor's business cycle model and its consequences,” Journal of Economic Behavior and Organization, vol. 24, no. 3, pp. 369–377, 1994. View at Google Scholar
  14. H. R. Varian, “Catastrophe theory and the business cycle,” Economic Inquiry, vol. 17, no. 1, pp. 14–28, 1979. View at Publisher · View at Google Scholar
  15. A. Kaddar and H. Talibi Alaoui, “Hopf bifurcation analysis in a delayed Kaldor-Kalecki model of business cycle,” Nonlinear Analysis: Modelling and Control, vol. 13, no. 4, pp. 439–449, 2008. View at Google Scholar · View at MathSciNet
  16. A. Agliari, R. Dieci, and L. Gardini, “Homoclinic tangles in a Kaldor-like business cycle model,” Journal of Economic Behavior and Organization, vol. 62, no. 3, pp. 324–347, 2007. View at Publisher · View at Google Scholar
  17. G. I. Bischi, R. Dieci, G. Rodano, and E. Saltari, “Multiple attractors and global bifurcations in a Kaldor-type business cycle model,” Journal of Evolutionary Economics, vol. 11, no. 5, pp. 527–554, 2001. View at Publisher · View at Google Scholar
  18. L. Wang and X. P. Wu, “Bifurcation analysis of a Kaldor-Kalecki model of business cycle with time delay,” Electronic Journal of Qualitative Theory of Differential Equations, no. 27, pp. 1–20, 2009. View at Google Scholar
  19. S. Ruan and J. Wei, “On the zeros of transcendental functions with applications to stability of delay differential equations with two delays,” Dynamics of Continuous, Discrete & Impulsive Systems, vol. 10, no. 6, pp. 863–874, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. T. Faria and L. T. Magalhães, “Normal forms for retarded functional-differential equations with parameters and applications to Hopf bifurcation,” Journal of Differential Equations, vol. 122, no. 2, pp. 181–200, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. T. Faria and L. T. Magalhães, “Normal forms for retarded functional-differential equations and applications to Bogdanov-Takens singularity,” Journal of Differential Equations, vol. 122, no. 2, pp. 201–224, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. Yu. Kuznetsov, Elements of Applied Bifurcation Theory, vol. 112 of Applied Mathematical Sciences, Springer, New York, NY, USA, 3rd edition, 2004. View at MathSciNet
  23. S. N. Chow, C. Li, and D. Wang, Normal Forms and Bifurcation of Planar Vector Fields, Cambridge University Press, Cambridge, UK, 2004.
  24. J. Carr, Applications of Centre Manifold Theory, vol. 35 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1981. View at Zentralblatt MATH · View at MathSciNet