Liu Zijian, Zhang Lei, Bi Ping, Pang Jianhua, Li Bing, Fang Chengling
a College of Mathematics and Statistics , Chongqing Jiaotong University , Chongqing , People's Republic of China.
b Department of Mathematics, Shanghai Key Laboratory of PMMP , East China Normal University , Shanghai , People's Republic of China.
J Biol Dyn. 2018 Dec;12(1):551-576. doi: 10.1080/17513758.2018.1485974.
In this paper, a one-prey-n-predator impulsive reaction-diffusion periodic predator-prey system with ratio-dependent functional response is investigated. On the basis of the upper and lower solution method and comparison theory of differential equation, sufficient conditions on the ultimate boundedness and permanence of the predator-prey system are established. By constructing an appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Examples and numerical simulations are presented to verify the feasibility of our results. A discussion is conducted at the end.
本文研究了一类具有比率依赖功能反应的单食饵 - n 捕食者脉冲反应扩散周期捕食 - 食饵系统。基于微分方程的上下解方法和比较理论，建立了捕食 - 食饵系统最终有界性和持久性的充分条件。通过构造一个合适的辅助函数，还得到了唯一全局稳定正周期解存在的条件。给出了例子和数值模拟以验证我们结果的可行性。最后进行了讨论。
