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

Hiromi Murakami (), Kazuo Nishimura and Tadashi Shigoka
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Hiromi Murakami: Osaka University

Chapter Chapter 8 in Sunspots and Non-Linear Dynamics, 2017, pp 175-200 from Springer

Abstract: 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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:steccp:978-3-319-44076-7_8

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DOI: 10.1007/978-3-319-44076-7_8

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