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Bifurcation structure in a bimodal piecewise linear business cycle model

Author

Listed:
  • Viktor Avrutin

    (DESP, University of Urbino and IST, University of Stuttgart, Germany)

  • Iryna Sushko

    (Institute of Mathematics, National Academy of Sciences of Ukraine)

  • Fabio Tramontana

    (Department of Economics and Management, University of Pavia)

Abstract

We study the bifurcation structure of the parameter space of a 1D continuous piecewise linear bimodal map which describes dynamics of a business cycle model introduced by Day-Shafer. In particular, we obtain the analytical expression of the boundaries of several periodicity regions associated with attracting cycles of the map (principal cycles and related ?n structure) crossing which the map has robust chaotic behavior.

Suggested Citation

  • Viktor Avrutin & Iryna Sushko & Fabio Tramontana, 2014. "Bifurcation structure in a bimodal piecewise linear business cycle model," DEM Working Papers Series 076, University of Pavia, Department of Economics and Management.
    • Handle: RePEc:pav:demwpp:demwp0076
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    References listed on IDEAS

    as
    1. Sushko, Iryna & Agliari, Anna & Gardini, Laura, 2006. "Bifurcation structure of parameter plane for a family of unimodal piecewise smooth maps: Border-collision bifurcation curves," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 756-770.
    2. Gardini, Laura & Sushko, Iryna & Naimzada, Ahmad K., 2008. "Growing through chaotic intervals," Journal of Economic Theory, Elsevier, vol. 143(1), pages 541-557, November.
    3. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
    4. Richard H. Day, 1994. "Complex Economic Dynamics - Vol. 1: An Introduction to Dynamical Systems and Market Mechanisms," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262041413, December.
    5. Day, Richard H. & Shafer, Wayne, 1987. "Ergodic fluctuations in deterministic economic models," Journal of Economic Behavior & Organization, Elsevier, vol. 8(3), pages 339-361, September.
    6. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-414, June.
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