一类具有相互干扰的功能反应捕食系统的捕获分析

Harvest analysis of a predator-prey system with mutual interference ' s functional response

研究一类具有相互干扰功能反应的捕食-食饵系统.对正平衡点的局部渐近稳定性和全局稳定进行了详细说明,证明了系统在正平衡点处是全局稳定的,并利用Pontrjagin最大值原理及最优控制理论,得到该系统的最优捕获策略.所得结果改进和推广了相关文献的主要结果.

In this paper, a predator-prey system with mutual interference and functional response is stud- ied. We local asymptotic stability and global stability of the positive equilibrium point. Hence we find that a locally stable positive equilibrium point must be a globally stable one. Using Pontryagin maximal princi- ple and optimizing control theory, we obtain the optimal harvesting policy. The results improve and gener- alize some previous results.