A note on the Bautin bifurcation in the modified Romer model with endogenous technical change

BELLA, GIOVANNI

2016-01-01

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Abstract

The aim of this paper is to present the necessary and sufficient conditions for the emergence of a generalized Hopf (i.e., Bautin) bifurcation in the modified version of the Romer [13] model of endogenous technical change with complementarity of intermediate goods, and determine the region of parameters where multiple attracting and repelling limit cycles around the steady-state may coexist. Interestingly, we show that a stable region of parameters exist where an unstable limit cycle is surrounded by a stable one; that is, the flow dynamic of the vector field returns to the stationary point for small disturbances though it becomes unstable, and exhibits persistent fluctuations, for larger parameter shocks.