Kar T K, Ghosh Bapan
Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah 711103, India.
Biosystems. 2012 Aug;109(2):220-32. doi: 10.1016/j.biosystems.2012.02.003. Epub 2012 Feb 25.
In the present paper, we develop a simple two species prey-predator model in which the predator is partially coupled with alternative prey. The aim is to study the consequences of providing additional food to the predator as well as the effects of harvesting efforts applied to both the species. It is observed that the provision of alternative food to predator is not always beneficial to the system. A complete picture of the long run dynamics of the system is discussed based on the effort pair as control parameters. Optimal augmentations of prey and predator biomass at final time have been investigated by optimal control theory. Also the short and large time effects of the application of optimal control have been discussed. Finally, some numerical illustrations are given to verify our analytical results with the help of different sets of parameters.
在本文中，我们构建了一个简单的两种群捕食者 - 猎物模型，其中捕食者部分地与替代猎物相耦合。目的是研究向捕食者提供额外食物的后果以及对两个物种施加捕捞努力的影响。据观察，向捕食者提供替代食物并不总是对系统有益。基于作为控制参数的努力对，讨论了系统长期动态的全貌。利用最优控制理论研究了最终时刻猎物和捕食者生物量的最优增加量。还讨论了应用最优控制的短期和长期影响。最后，给出了一些数值示例，借助不同的参数集来验证我们的分析结果。
