Kuwamura Masataka, Nakazawa Takefumi, Ogawa Toshiyuki
Graduate School of Human Development and Environment, Kobe University, Kobe, 657-8501, Japan.
J Math Biol. 2009 Mar;58(3):459-79. doi: 10.1007/s00285-008-0203-1. Epub 2008 Jul 29.
In this paper, a mathematical model of a prey-predator system is proposed to resolve the paradox of enrichment in ecosystems. The model is based on the natural strategy that a predator takes, i.e, it produces resting eggs in harsh environment. Our result gives a criterion for a functional response, which ensures that entering dormancy stabilizes the population dynamics. It is also shown that the hatching of resting eggs can stabilize the population dynamics when the switching between non-resting and resting eggs is sharp. Furthermore, the bifurcation structure of our model suggests the simultaneous existence of a stable equilibrium and a large amplitude cycle in natural enriched environments.
本文提出了一个捕食者 - 猎物系统的数学模型，以解决生态系统中的富集悖论。该模型基于捕食者采取的自然策略，即在恶劣环境中产生休眠卵。我们的结果给出了一个功能反应的准则，该准则确保进入休眠状态能稳定种群动态。研究还表明，当非休眠卵和休眠卵之间的转换很突然时，休眠卵的孵化可以稳定种群动态。此外，我们模型的分岔结构表明，在自然富集环境中，稳定平衡点和大幅度周期会同时存在。
