A general classification of the replication dynamics with a unique fixed point in the interior of simplex $S_N$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917500780806144 |
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| author | Chen, Hongju Daisy Yi, Bin Ma, Zhanshan Sam |
| author_facet | Chen, Hongju Daisy Yi, Bin Ma, Zhanshan Sam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13883 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A general classification of the replication dynamics with a unique fixed point in the interior of simplex $S_N$ Chen, Hongju Daisy Yi, Bin Ma, Zhanshan Sam Populations and Evolution Computer Science and Game Theory Multiagent Systems 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. |
| title | A general classification of the replication dynamics with a unique fixed point in the interior of simplex $S_N$ |
| topic | Populations and Evolution Computer Science and Game Theory Multiagent Systems |
| url | https://arxiv.org/abs/2605.13883 |