英国本土物种红松鼠正面临灭绝危机,而灰松鼠数量日益增多. 针对目前状况,文章根据灰松鼠或红松鼠数量来投放药物治理红松鼠身上病毒,和捕获灰松鼠的治理办法.即考虑一类竞争状态脉冲微分方程模型,利用后继函数法和微分方程有关理论,获得了系统存在阶$1$周期解的充分条件,即在一定条件下红松鼠灰松鼠是持续生存的,所得结论对红松鼠保护和为英国本土的生态平衡提供一定的理论依据.数值分析也进一步说明系统的动力学性质.

The number of red squirrels of British native species is facing extinctcrisis, and the number of gray squirrels is increasing. In view of the above situation,
we increase the number of red squirrels by putting on medication to control body’s virus of red squirrels and reduce the number of gray squirrels by capturing gray squirrels. That is, we consider a class of model with competitive and state-dependent impulsive differential equations and obtain sufficient conditions of the investigated system with periodic solution of order one by using the successor function method and the related differential equations theory. Therefore, red squirrels and gray squirrels are permanence under certain conditions. The results provide reliable theoretical basis for protection of red squirrels and the ecological balance of the United Kingdom. Finally, numerical analysis also illustrates the nature of the dynamic system.