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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 4021516, 8 pages
Research Article

Convergence of Global Solutions to the Cauchy Problem for the Replicator Equation in Spatial Economics

1Department of Mathematical Sciences, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan
2Department of Statistics, Oita University, Oita 879-5593, Japan

Received 21 March 2016; Accepted 29 June 2016

Academic Editor: Douglas R. Anderson

Copyright © 2016 Minoru Tabata and Nobuoki Eshima. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the initial-value problem for the replicator equation of the -region Core-Periphery model in spatial economics. The main result shows that if workers are sufficiently agglomerated in a region at the initial time, then the initial-value problem has a unique global solution that converges to the equilibrium solution expressed by full agglomeration in that region.