Strong solutions and instability for the fitness gradient system in evolutionary games between two populations

Qiuju Xu, Andrew Belmonte, Russ deForest, Chun Liu, Zhong Tan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper, we study a fitness gradient system for two populations interacting via a symmetric game. The population dynamics are governed by a conservation law, with a spatial migration flux determined by the fitness. By applying the Galerkin method, we establish the existence, regularity and uniqueness of global solutions to an approximate system, which retains most of the interesting mathematical properties of the original fitness gradient system. Furthermore, we show that a Turing instability occurs for equilibrium states of the fitness gradient system, and its approximations.

Original languageEnglish (US)
Pages (from-to)4021-4051
Number of pages31
JournalJournal of Differential Equations
Volume262
Issue number7
DOIs
StatePublished - Apr 5 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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