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arXiv · 2605.13883

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

Hongju Daisy Chen·Bin Yi·Zhanshan Sam Ma
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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 $S_n$(Int$S_n$) for $n\geq 2$ are presented. Furthermore, the different types of replication dynamics equations with a unique fixed point in IntSn is discussed.

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Hongju Daisy Chen, Bin Yi, Zhanshan Sam Ma. 2026-05-11. A general classification of the replication dynamics with a unique fixed point in the interior of simplex $S_N$. https://arxiv.org/abs/2605.13883

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