污染环境下具有尺度结构的捕食种群系统的最优控制

doi:10.6040/j.issn.1671-9352.0.2024.393

摘要/Abstract

摘要： 研究一类污染环境下依赖个体尺度的捕食种群系统的最优控制问题, 其控制变量为生育率与毒素的输入量。运用切锥法锥理论、Dubovitskii-Milyutin定理和共轭系统技巧分别给出固定时间区间上的端点自由问题、无穷时间问题、状态约束问题的最优性条件,为治理环境污染、保护生物多样性、科学开发生物资源等方面提供理论支撑。

关键词: 环境污染, 尺度结构, 最优控制, 共轭系统

Abstract: We investigate the optimal control problem for a predator-prey system that depends on individual size in a polluted environment. The control variables include fertility and the input rate of exogenous toxicants. The optimality conditions for various problems-free terminal, infinite horizon, and constrained end point problem on fixed horizon-are derived using the theory of tangent-normal cones, the Dubovitskii-Milyutin theorem, and the adjoint system technique. These results offer theoretical underpinnings for controlling environmental pollution, protecting biodiversity, and scientifically exploiting biological resources.

Key words: environmental pollution, size structure, optimal control, adjoint system

中图分类号:

O232

张泰年. 污染环境下具有尺度结构的捕食种群系统的最优控制[J]. 《山东大学学报(理学版)》, 2026, 61(7): 108-122.

ZHANG Tainian. Optimal control for predator-prey system with size structure in a polluted environment[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(7): 108-122.

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