相互作用复制者动力学中的持久性与中性
Persistence and neutrality in interacting replicator dynamics
AI总结：
研究遵循类复制者随机动力学的实体集合大时间行为，证明混沌传播性质与系统强持久性条件，发现适应度等效性作为持久性条件自然涌现且中性与唯一Dirichlet不变测度相关。
摘要：
我们研究遵循类复制者随机动力学且具有平均场相互作用的实体集合的大时间行为，作为原始生态学模型。我们证明了混沌传播性质，并建立了 N-复制者系统强持久性的条件以及一类相关 McKean-Vlasov 动力学不变分布的存在性。特别地，我们的结果表明，与典型的中性生态学模型不同，适应度等效性无需假设，而是作为系统持久性的条件自然涌现。此外，中性与唯一的 Dirichlet 不变概率测度相关联。我们用简单案例研究说明发现，提供数值结果，并基于生态学中性理论讨论结论。
英文摘要：
We study the large-time behavior of an ensemble of entities obeying replicator-like stochastic dynamics with mean-field interactions as a model for a primordial ecology. We prove the propagation-of-chaos property and establish conditions for the strong persistence of the $N$-replicator system and the existence of invariant distributions for a class of associated McKean-Vlasov dynamics. In particular, our results show that, unlike typical models of neutral ecology, fitness equivalence does not need to be assumed but emerges as a condition for the persistence of the system. Further, neutrality is associated with a unique Dirichlet invariant probability measure. We illustrate our findings with some simple case studies, provide numerical results, and discuss our conclusions in the light of Neutral Theory in ecology.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
