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周期环境中捕食者具有尺度结构的三物种捕食-食饵系统的最优收获

刘荣 刘桂荣

刘荣, 刘桂荣. 周期环境中捕食者具有尺度结构的三物种捕食-食饵系统的最优收获[J]. 应用数学和力学, 2021, 42(5): 510-521. doi: 10.21656/1000-0887.410285
引用本文: 刘荣, 刘桂荣. 周期环境中捕食者具有尺度结构的三物种捕食-食饵系统的最优收获[J]. 应用数学和力学, 2021, 42(5): 510-521. doi: 10.21656/1000-0887.410285
LIU Rong, LIU Guirong. Optimal Harvesting in a Periodic 3-Species Predator-Prey Model With Size Structure in Predators[J]. Applied Mathematics and Mechanics, 2021, 42(5): 510-521. doi: 10.21656/1000-0887.410285
Citation: LIU Rong, LIU Guirong. Optimal Harvesting in a Periodic 3-Species Predator-Prey Model With Size Structure in Predators[J]. Applied Mathematics and Mechanics, 2021, 42(5): 510-521. doi: 10.21656/1000-0887.410285

周期环境中捕食者具有尺度结构的三物种捕食-食饵系统的最优收获

doi: 10.21656/1000-0887.410285
基金项目: 国家自然科学基金(12001341;11971279);山西省青年科技研究基金(201901D211410);山西省高等学校科技创新项目(2020L0258)
详细信息
    作者简介:

    刘荣(1988—),男,博士(E-mail: rliu29@sxufe.edu.cn);刘桂荣(1975—),男,教授,博士生导师(通讯作者. E-mail: lgr5791@sxu.edu.cn).

  • 中图分类号: O175.22

Optimal Harvesting in a Periodic 3-Species Predator-Prey Model With Size Structure in Predators

Funds: The National Natural Science Foundation of China(12001341;11971279)
  • 摘要: 对种群动力学及相关控制问题的研究,不仅具有理论意义,而且与生物多样性保护、病虫害防治及可再生资源的开发利用密切相关.该文研究了一类周期环境中具有两相互竞争食饵和一捕食者的三物种捕食食饵系统的最优收获,其中捕食者具有尺度结构且用一阶偏微分方程描述.运用不动点定理证明了系统非负有界解的存在唯一性,并讨论了解关于控制变量的连续依赖性.应用切法锥技巧导出最优收获条件,并借助Ekeland变分原理讨论了最优策略的存在唯一性.这里目标泛函表示收获三物种产生的净经济效益.所得结果将有利于可再生资源的开发.
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出版历程
  • 收稿日期:  2020-09-21
  • 修回日期:  2021-03-12
  • 刊出日期:  2021-05-01

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