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Break and sustain bifurcations of S_N-invariant equidistant economy

Hiroki Aizawa, Kiyohiro Ikeda, Minoru Osawa () and Gasper José M

MPRA Paper from University Library of Munich, Germany

Abstract: This paper aims at the elucidation of the bifurcation mechanism of an equidistant economy in Economic Geography. An attention is paid to the existence of invariant solutions that retain their spatial patterns when the bifurcation parameter changes. Theoretical results on symmetrybreaking bifurcation of the symmetric group SN, which describes the symmetry of this economy, is combined with the mechanism of sustain bifurcation of invariant patterns that is inherent to the economy. The stability of bifurcating branches is investigated theoretically to demonstrate that most of them are asymptotically unstable. Among a plethora of theoretically possible spatial patterns, those which actually become stable for spatial economic models are investigated numerically. The solution curves of the economy are shown to display a complicated mesh-like structure, which looks like threads of warp and weft.

Keywords: Bifurcation; equidistant economy; group-theoretic bifurcation theory, invariant pattern, replicator dynamics, spatial economic model, stability (search for similar items in EconPapers)
JEL-codes: R12 (search for similar items in EconPapers)
Date: 2019-06-19
New Economics Papers: this item is included in nep-geo
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https://mpra.ub.uni-muenchen.de/97761/1/MPRA_paper_97654.pdf revised version (application/pdf)

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