极限环上的脉冲收获控制

Pulse harvesting control on limit rings

具有Holling II功能项的捕食模型研究广泛,基于捕食模型的状态脉冲控制也有分析.然而这些研究的内容大部分局限于内部平衡点稳定性的情况下.在实际环境中,被捕食者和捕食者并不是最终趋于稳定的,存在着被捕食者趋于零导致捕食者急剧减少的情况.针对上述情况,讨论了当系统存在唯一不稳定的内部平衡点时,分析捕食者和被捕食者的关系,进而通过环域定理分析出了极限环的存在唯一性.为了达到最大的经济利益和维护生态的平衡,进一步研究了在极限环存在的情况下的状态反馈系统.通过后继函数得到了阶一周期解的存在性,通过极限集得到了阶一周期解的稳定性.

With functions of Holling Ⅱ predator - prey model discussed widely, status of the pulse control feeding model were also analyzed. However, the content of these studies branch largely confined to the internal stability of equilibrium point. In a real environment, prey and predator is not ultimately tend to be stable, there is a lead to sharply reduce predator prey tends to zero. According to the above situation, this paper discussed the system exists only unstable internal balance, and the relationship between predator and prey, and the theorem Bendix - son ring domain analysis the existence and uniqueness of limit cycle. In order to a- chieve maximum economic benefits and maintain ecological balance, under the condition of the limit cycle was further studied the status of the feedback system. Via the successor func- tions at the same time, got the existence of order- 1 periodic solutions for impulsive system and the stabilitv of order - 1 periodic solutions by limit set.