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.

Tramontana, F., Sushko, I., Avrutin, V., Period adding structure in a 2D discontinuous model of economic growth, <<APPLIED MATHEMATICS AND COMPUTATION>>, 2015; 253 (N/A): 262-273. [doi:10.1016/j.amc.2014.12.078] [http://hdl.handle.net/10807/67390]

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

Tramontana, Fabio;
2015

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.
Inglese
Tramontana, F., Sushko, I., Avrutin, V., Period adding structure in a 2D discontinuous model of economic growth, <<APPLIED MATHEMATICS AND COMPUTATION>>, 2015; 253 (N/A): 262-273. [doi:10.1016/j.amc.2014.12.078] [http://hdl.handle.net/10807/67390]
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