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Period adding structure in a 2D discontinuous model of economic growth

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  • Tramontana, Fabio
  • Sushko, Iryna
  • Avrutin, Viktor

Abstract

We study the dynamics of a growth model formulated in the tradition of Kaldor and Pasinetti where the accumulation of the ratio capital/workers is regulated by a two-dimensional discontinuous map with triangular structure. We determine analytically the border collision bifurcation boundaries of periodicity regions related to attracting cycles, showing that in a two-dimensional parameter plane these regions are organized in the period adding structure. We show that the cascade of flip bifurcations in the base one-dimensional map corresponds for the two-dimensional map to a sequence of pitchfork and flip bifurcations for cycles of even and odd periods, respectively.

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  • Tramontana, Fabio & Sushko, Iryna & Avrutin, Viktor, 2015. "Period adding structure in a 2D discontinuous model of economic growth," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 262-273.
    • Handle: RePEc:eee:apmaco:v:253:y:2015:i:c:p:262-273
    DOI: 10.1016/j.amc.2014.12.078
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    Cited by:

    1. Gardini, Laura & Sushko, Iryna & Tramontana, Fabio, 2021. "Dynamics of a two-dimensional map on nested circles and rings," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Sushko, Iryna & Gardini, Laura & Matsuyama, Kiminori, 2019. "Dynamics of a generalized fashion cycle model," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 135-147.
    3. Laura Gardini & Iryna Sushko & Kiminori Matsuyama, 2017. "2D discontinuous piecewise linear map: Emergence of fashion cycles," Working Papers 1703, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2017.

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