论文标题
最佳收获生物模型的动力学
The Dynamics of Biological models with Optimal Harvesting
论文作者
论文摘要
本文旨在介绍动态系统平衡点的概念，该概念将其称为几乎全球渐近稳定。还分析了猎物物种的修饰功能增长，也分析了生物猎物侵害模型。给出了局部稳定的条件及其所有均衡的存在。之后，将模型扩展到最佳控制问题，以获得最佳的收获策略。 Pontryagin的最大原理的离散时间版本用于解决最佳问题。得出了最佳收获变量和伴随变量的表征。最后，提供了各种参数值的数值模拟，以确认理论发现。
This paper aims to introduce a concept of an equilibrium point of a dynamical system which will call it almost global asymptotically stable. A biological prey-predator model is also analyzed with a modification function growth in prey species. The conditions of the local stable and existence of all its equilibria are given. After that the model is extended to an optimal control problem to obtain an optimal harvesting strategy. The discrete time version of Pontryagin's maximum principle is applied to solve the optimality problem. The characterization of the optimal harvesting variable and the adjoint variables are derived. Finally numerical simulations of various set of values of parameters are provided to confirm the theoretical findings.
