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

Author

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  • Nishimura Kazuo

    (Research Institute for Economics and Business Administration, Kobe University, Kobe, Japan)

  • Shigoka Tadashi

    (Institute of Economic Research, Kyoto University, Kyoto, Japan)

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.

Suggested Citation

  • Nishimura Kazuo & Shigoka Tadashi, 2019. "Hopf bifurcation and the existence and stability of closed orbits in three-sector models of optimal endogenous growth," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(4), pages 1-21, September.
    • Handle: RePEc:bpj:sndecm:v:23:y:2019:i:4:p:21:n:1
    DOI: 10.1515/snde-2019-0017
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    Cited by:

    1. Takuma Kunieda & Kazuo Nishimura, 2021. "Pollution, Human Capital, and Growth Cycles," Creative Economy, in: Kazuo Nishimura & Masatoshi Murase & Kazuyoshi Yoshimura (ed.), Creative Complex Systems, chapter 0, pages 85-99, Springer.
    2. Marco Desogus & Beatrice Venturi, 2023. "Stability and Bifurcations in Banks and Small Enterprises—A Three-Dimensional Continuous-Time Dynamical System," JRFM, MDPI, vol. 16(3), pages 1-20, March.

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