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

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.