Papers

Jun 15, 2019

Invariant Patterns for Replicator Dynamics on a Hexagonal Lattice

International Journal of Bifurcation and Chaos
  • K. Ikeda
  • ,
  • Y. Kogure
  • ,
  • H. Aizawa
  • ,
  • Y. Takayama

Volume
29
Number
06
First page
1930014
Last page
1930014
Language
Publishing type
Research paper (scientific journal)
DOI
10.1142/s0218127419300143
Publisher
World Scientific Pub Co Pte Lt

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.

Link information
DOI
https://doi.org/10.1142/s0218127419300143
URL
https://www.worldscientific.com/doi/pdf/10.1142/S0218127419300143
ID information
  • DOI : 10.1142/s0218127419300143
  • ISSN : 0218-1274
  • eISSN : 1793-6551

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