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Break and sustain bifurcations of S_N-invariant equidistant economy

Aizawa, Hiroki and Ikeda, Kiyohiro and Osawa, Minoru and Gaspar, José M. (2019): Break and sustain bifurcations of S_N-invariant equidistant economy.

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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.

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