Breaking and Sustaining Bifurcations in SN-Invariant Equidistant Economy

H. Aizawa, K. Ikeda, M. Osawa, J. M. Gaspar

Research output: Contribution to journalArticlepeer-review

Abstract

This paper elucidates the bifurcation mechanism of an equidistant economy in spatial economics. To this end, we derive the rules of secondary and further bifurcations as a major theoretical contribution of this paper. Then we combine them with pre-existing results of direct bifurcation of the symmetric group SN [Elmhirst, 2004]. Particular attention is devoted to the existence of invariant solutions which retain their spatial distributions when the value of the bifurcation parameter changes. Invariant patterns of an equidistant economy under the replicator dynamics are obtained. The mechanism of bifurcations from these patterns is elucidated. The stability of bifurcating branches is analyzed to demonstrate that most of them are unstable immediately after bifurcation. Numerical analysis of spatial economic models confirms that almost all bifurcating branches are unstable. Direct bifurcating curves connect the curves of invariant solutions, thereby creating a mesh-like network, which appears as threads of warp and weft. The theoretical bifurcation mechanism and numerical examples of networks advanced herein might be of great assistance in the study of spatial economics.

Original languageEnglish
Article number2050240
JournalInternational Journal of Bifurcation and Chaos
Volume30
Issue number16
DOIs
Publication statusPublished - 2020 Dec 30

Keywords

  • Bifurcation
  • equidistant economy
  • group-theoretic bifurcation theory
  • invariant pattern
  • replicator dynamics
  • spatial economic model
  • stability

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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