English

A general classification of the replication dynamics with a unique fixed point in the interior of simplex $S_N$

Populations and Evolution 2026-05-18 v1 Computer Science and Game Theory Multiagent Systems

Abstract

The replication dynamics (differential equation system) is the foundation of evolutionary game theory. When n=2, there are four possible types of replication dynamics. When n=3, there are 49 possible types of replication dynamics. However, when n>3, the classification of replication dynamics has not been solved. In this article, the sufficient and necessary conditions of the replication dynamics equation with a unique fixed point in the interior of simplex SnS_n(IntSnS_n) for n2n\geq 2 are presented. Furthermore, the different types of replication dynamics equations with a unique fixed point in IntSn is discussed.

Keywords

Cite

@article{arxiv.2605.13883,
  title  = {A general classification of the replication dynamics with a unique fixed point in the interior of simplex $S_N$},
  author = {Hongju Daisy Chen and Bin Yi and Zhanshan Sam Ma},
  journal= {arXiv preprint arXiv:2605.13883},
  year   = {2026}
}