两区域分数阶捕食者–猎物种群模型的参数反问题
Parameter Inverse Problem of the Two-Patch Fractional Predator-Prey Population Model
摘要: 本文考虑分数阶捕食者–猎物种群模型以及该模型的参数反问题。介绍正问题解的存在性与唯一性，提出了微分阶数和生长速率的反问题，并对反问题解的存在唯一性给出了证明。利用有限差分法求解正问题获得附加数据，然后根据同伦正则化算法进行参数的数值反演，数值结果表明该算法能够有效求解分数阶捕食者–猎物种群模型参数反问题。
Abstract: This paper considers the fractional predator-prey population model and the parameter inverse problem of the model. The existence and uniqueness of forward problem solutions are introduced, the inverse problems of differential order and growth rate are proposed, and the existence and uniqueness of inverse problem solutions is proved. The finite difference method is used to solve the positive problem to obtain additional data, and then numerically inverse the parameters according to the homotopy regularization algorithm. The numerical results show that the algorithm can effectively solve the parameter inverse problem of the fractional predator-prey population model.
文章引用：施芳, 张应洪, 刘雪林. 两区域分数阶捕食者–猎物种群模型的参数反问题[J]. 应用数学进展, 2024, 13(6): 2595-2604. https://doi.org/10.12677/aam.2024.136248

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