Department of Mathematics, University Institute of Technology, Burdwan University, Burdwan, India.
J Biol Dyn. 2009 Sep;3(5):447-62. doi: 10.1080/17513750802560346.
This paper deals with the problem of non-selective harvesting of a prey-predator system by using a reasonable catch-rate function instead of usual catch-per-unit-efforthypothesis. Here both the prey and the predator species obey the law of logistic growth. We have taken the predator functional response to prey density in such a form that each predator's functional response to the prey density approaches a constant as the prey population increases. Boundedness of the exploited system is examined. The existence of its steady states and their stability (local and global) are studied using Eigenvalue analysis. The existence of bionomic equilibria has been illustrated using a numerical example. The problem of determining the optimal harvesting policy is then solved by using Pontryagin's maximum principle.
本文研究了使用合理的捕捞率函数而非通常的单位捕捞努力量假说来实现猎物-捕食者系统非选择性捕捞的问题。在这里，猎物和捕食者物种都遵循逻辑斯谛增长规律。我们采用了这样一种捕食者对猎物密度的功能反应形式，即随着猎物种群的增加，每个捕食者对猎物密度的功能反应趋近于一个常数。研究了被开发系统的有界性。利用特征值分析研究了其平衡点的存在及其稳定性（局部和全局）。通过数值例子说明了生物平衡的存在。然后，利用庞特里亚金极大值原理解决了最优捕捞策略的确定问题。
