AI 中文总结
构建含环境因素影响的随机微分方程模型（非利普希茨扩散系数的扩散桥），通过时变产生随机初末时间，建立模型适定性，依水温影响鱼洄游假设估算参数并探索环境DNA数据分析应用。
AI 中文摘要
我们对在随机环境中沿河流固定位置观测到的洄游鱼类数量动态进行数学建模。特别地，作为一种新方法，我们构建了一个包含环境因素对洄游开始和结束波动影响的随机微分方程。该模型是具有非利普希茨扩散系数的扩散桥，称为考克斯 - 英格索尔 - 罗斯桥，并且具有由时间变化产生的随机初始和终止时间，以便能够有效地纳入环境因素的影响。首先建立了模型的适定性，这在应用数学中被认为是新颖且重要的。其次，我们基于最新的多年每日数据集，通过依赖水温影响鱼类洄游这一在现有研究中已被提出的假设，来估计模型的参数。我们还探索了所提出模型在分析环境DNA数据这一具有挑战性任务中的应用。本研究推动了一种简单但能考虑环境因素的鱼类洄游理论的发展。
英文摘要
We mathematically model the dynamics of the number of migratory fish observed at a fixed location along a river in a random environment. Particularly, as a new approach, we construct a stochastic differential equation that incorporates the influence of environmental factors on the fluctuations in the start and end of migration. The model is a diffusion bridge with a non-Lipschitz diffusion coefficient, called the Cox-Ingersoll-Ross bridge, and has random initial and terminal times arising from time-change, so that the influences of environmental factors can be efficiently incorporated. The well-posedness of the model is first established, which is considered novel and significant in applied mathematics. Second, we estimate the parameters of the model based on the latest multiyear daily data set for the upstream migration of Plecoglossus altivelis altivelis (Ayu) by relying on the hypothesis that water temperature affects the migration of the fish, which has been suggested in existing studies. We also explore the application of the proposed model to the challenging task of analyzing environmental DNA data. This study advances the development of a theory of fish migration that is simple yet can take environmental factors into account.
CommentsUpdated on August 17, 2026
DOI：10.1016/j.chaos.2026.119116
