Invariant patterns for replicator dynamics on a hexagonal lattice

K. Ikeda, Y. Kogure, H. Aizawa, Yuki Takayama

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


A hexagonal lattice is a promising and plausible spatial platform for economic agglomeration in spatial economic models. This paper aims at the elucidation of agglomeration mechanisms for the replicator dynamics on this lattice. Attention is paid to the existence of invariant solutions that retain their spatial patterns when the bifurcation parameter changes. Such existence is a special feature of the replicator dynamics, which is widely used in economics. A theoretical procedure to find invariant patterns is proposed and possible invariant patterns are advanced and classified. Among a plethora of theoretically possible invariant patterns, those which actually become stable for a spatial economic model are investigated numerically. The major finding of this paper, is the demonstration of equilibrium curves of invariant patterns that are connected by those of noninvariant ones to form a complicated mesh-like structure, just like the threads of warp and weft. It would be an important scientific mission to elucidate the mechanism of this complicated structure, and contribute to the study in economic geography.

Original languageEnglish
Article number1930014
JournalInternational Journal of Bifurcation and Chaos
Issue number6
Publication statusPublished - 2019 Jun 15


  • Bifurcation
  • group-Theoretic bifurcation theory
  • hexagonal lattice
  • invariant pattern
  • replicator dynamics
  • spatial economic model

ASJC Scopus subject areas

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


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