Comprehending life history of migratory fish, onset of migration in particular, is a key biological and ecological research topic that still has not been clarified. In this paper, we propose a simple mathematical model for the onset of fish migration in the context of a stochastic optimal stopping theory, which is a new attempt to our knowledge. Finding the criteria of the onset of migration reduces to solving a variational inequality of a degenerate elliptic type. As a first step of the new mathematical modeling, mathematical and numerical analyses with particular emphasis on whether the model is consistent with the past observation results of fish migration are examined, demonstrating reasonable agreement between the theory and observation results. The present mathematical model thus potentially serves as a simple basis for analyzing onset of fish migration.

中文翻译：

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阻止鱼类迁移的最佳方法。

理解迁徙鱼类的生活史，尤其是迁移的开始，是一个关键的生物学和生态学研究主题，目前尚未阐明。在本文中，我们提出了一种基于随机最优停止理论的鱼类迁移开始的简单数学模型，这是我们所知的新尝试。寻找迁移开始的标准可简化为解决退化椭圆型的变分不等式。作为新的数学建模的第一步，对数学和数值分析进行了重点研究，特别是该模型是否与过去的鱼类迁移观察结果一致，这证明了理论与观察结果之间的合理一致性。