The Hopf Bifurcation and the Existence and Stability of Closed Orbits in Multisector Models of Optimal Economic Growth

2021 ◽  
pp. 206-227
Author(s):  
JESS BENHABIB ◽  
KAZUO NISHIMURA
Keyword(s):  
Economic Growth ◽  
Hopf Bifurcation ◽  
Closed Orbits ◽  
Existence And Stability ◽  
Optimal Economic Growth

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

2019 ◽  
Vol 23 (4) ◽  
Author(s):  
Kazuo Nishimura ◽  
Tadashi Shigoka
Keyword(s):  
Hopf Bifurcation ◽  
Endogenous Growth ◽  
Bifurcation Analysis ◽  
Stable Manifold ◽  
Closed Orbit ◽  
One Dimensional ◽  
Convex Structure ◽  
Equilibrium Dynamics ◽  
Closed Orbits ◽  
Existence And Stability

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.

Essays on the Theory of Optimal Economic Growth.

1968 ◽  
Vol 78 (311) ◽  
pp. 672 ◽  
Author(s):  
A. B. Atkinson ◽  
K. Shell
Keyword(s):  
Economic Growth ◽  
Optimal Economic Growth
Sign in / Sign up

Export Citation Format

Share Document