Chandrahati Dilip Kumar High School (H.S.), Chandrahati 712504, West Bengal, India.
Math Biosci. 2013 Feb;241(2):181-7. doi: 10.1016/j.mbs.2012.11.007. Epub 2012 Dec 3.
The paper presents the study of one prey one predator harvesting model with imprecise biological parameters. Due to the lack of precise numerical information of the biological parameters such as prey population growth rate, predator population decay rate and predation coefficients, we consider the model with imprecise data as form of an interval in nature. Many authors have studied prey-predator harvesting model in different form, here we consider a simple prey-predator model under impreciseness and introduce parametric functional form of an interval and then study the model. We identify the equilibrium points of the model and discuss their stabilities. The existence of bionomic equilibrium of the model is discussed. We study the optimal harvest policy and obtain the solution in the interior equilibrium using Pontryagin's maximum principle. Numerical examples are presented to support the proposed model.
本文研究了一类具有不精确生物参数的单猎物一单捕食者收获模型。由于缺乏猎物种群增长率、捕食者种群衰减率和捕食系数等生物参数的精确数值信息，我们将模型中的不精确数据视为自然形式的区间。许多作者已经研究了不同形式的猎物-捕食者收获模型，在这里我们考虑了不精确条件下的一个简单的猎物-捕食者模型，并引入了区间的参数函数形式，然后对模型进行了研究。我们确定了模型的平衡点，并讨论了它们的稳定性。讨论了模型的生态平衡点的存在性。我们研究了最优收获策略，并使用庞特里亚金极大值原理在内部平衡点处得到了解析解。给出了数值例子来支持所提出的模型。
