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Homoclinic Orbit and Stationary Sunspot Equilibrium in a Three-Dimensional Continuous-Time Model with a Predetermined Variable

In: Sunspots and Non-Linear Dynamics

Author

Listed:
  • Hiromi Murakami

    (Osaka University)

  • Kazuo Nishimura

    (Kobe University)

  • Tadashi Shigoka

    (Kyoto University)

Abstract

We treat a three-dimensional continuous-time model that includes one predetermined variable and two non-predetermined variables. We assume (1) that the model has a two-dimensional well-located invariant manifold and (2) that the manifold includes a one-dimensional closed curve that could be either a homoclinic orbit or a closed orbit. We construct a stationary sunspot equilibrium in this three-dimensional model by means of generalizing the methods due to Nishimura and Shigoka (2006) and Benhabib et al. (2008). By appealing to the same argument as in Nishimura and Shigoka (2006) we can apply our result to some variants of the Lucas (1988) model the transitional dynamics of which is three-dimensional and undergoes homoclinic bifurcation.

Suggested Citation

  • Hiromi Murakami & Kazuo Nishimura & Tadashi Shigoka, 2017. "Homoclinic Orbit and Stationary Sunspot Equilibrium in a Three-Dimensional Continuous-Time Model with a Predetermined Variable," Studies in Economic Theory, in: Kazuo Nishimura & Alain Venditti & Nicholas C. Yannelis (ed.), Sunspots and Non-Linear Dynamics, chapter 0, pages 175-200, Springer.
    • Handle: RePEc:spr:steccp:978-3-319-44076-7_8
    DOI: 10.1007/978-3-319-44076-7_8
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