Large-dimensional replicator equations with antisymmetric random interactions
Large-dimensional replicator equations with antisymmetric random interactions
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DOI：
10.1143/jpsj.71.429
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发表时间：
2002-02-01
影响因子：
1.7
通讯作者：
Tokita, K
中科院分区：
文献类型：
--
作者：
Chawanya, T;Tokita, K
我们研究了有效自由度的渐近行为（即，研究了具有猝灭反对称随机种间相互作用的高维复制子方程（RE）的解.研究发现，当随机相互作用是反对称的时，系统的多样性保持在初始多样性N的量级，而当随机相互作用是对称的或非对称的时，系统的多样性通过“消光”迅速下降到1阶.在反对称情形下，一个唯一吸引集的全局稳定性与一般具有许多吸引子的对称和非对称情形进行了对比。这一结果为解决“生态学悖论”提供了一种新的维持生物多样性的机制。
We study the asymptotic behavior of effective degrees of freedom (i.e., the number of species or the diversity) of large-dimensional replicator equations (RE) with quenched antisymmetric random interspecies interactions. It is found that the diversity is maintained at the order of initial diversity N if the random interactions are antisymmetric, while it is known that the diversity rapidly decreases to order 1 via "extinction" in the RE with symmetric or asymmetric random quenched interactions. In the antisymmetric case, the global stability of a unique attracting set is contrasted to the symmetric and asymmetric cases which have many attractors in general. The present result suggests a new mechanism of maintaining biodiversity which resolves the "paradox of ecology".