Hopf bifurcation and the existence and stability of closed orbits in three-sector models of optimal endogenous growth

Kazuo Nishimura and Tadashi Shigoka

Studies in Nonlinear Dynamics & Econometrics, 2019, vol. 23, issue 4, 21

Abstract: The present paper constructs a family of three-sector models of optimal endogenous growth, and conducts exact bifurcation analysis. In so doing, original six-dimensional equilibrium dynamics is decomposed into five-dimensional stationary autonomous dynamics and one-dimensional endogenously growing component. It is shown that the stationary dynamics thus decomposed undergoes supercritical Hopf bifurcation. It is inferred from the convex structure of our model that the dimension of a stable manifold of each closed orbit thus bifurcated in this five-dimensional dynamics should be two.

Keywords: Hopf bifurcation; multi-sector model; optimal endogenous growth model (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1515/snde-2019-0017

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