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

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.