具有避难所的捕食者-被捕食者模型的动力学行为
Dynamics of a harvested prey-predator model with prey refuge depended on both species
摘要：
本文研究了一类食饵避难所比例为两种群的食饵-捕食者模型，其中各种群的收获是独立的。我们的研究表明，利用避难所作为控制，可以突破系统的极限环，达到所需的平衡水平状态。建立了最优收获策略。确定了系统内部平衡点的有界性、可行性和生态平衡点。主要的观察是，避难所系数起着重要的作用，在调节本系统的动态。避难所系数的变化使系统由稳定变为不稳定，反之亦然。为了支持我们的分析和理论研究结果，给出了一些数值例子。
英文摘要：
The present paper deals with a prey-predator model with prey refuge proportion to both species and independent harvesting of each species. Our study shows that using refuge as control, it can break the limit circle of the system and reach the required state of equilibrium level. It is established the optimal harvesting policy. The boundedness, feasibility of interior equilibria, bionomic equilibrium have been determined. The main observation is that coefficient of refuge plays an important role in regulating the dynamics of the present system. Moreover the variation of the coefficient of refuge change the system from stable to unstable and vice-versa. Some numerical illustration are given in order to support of our analytical and theoretical findings.
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