基于脉冲微分方程研究具有竞争关系的捕食系统的持久性

The Permanence of the Predator-prey System is Studied Based on Impulsive Differential Equations

基于脉冲微分方程理论,考虑到在现实生活中,种群内部和种群之间都存在相互竞争,故本文在捕食与被捕食系统中引入竞争关系,建立了具有Hassell-Varley功能性反应的一类食饵与一类捕食者系统.利用比较定理得到此系统的有界性和生物学家比较关注的系统持久性的充分条件,即定理3.1和定理3.2.最后本文对得到的结论进行了阐释,并给出了相应的生物学意义.

Based on the theory of impulsive differential equation,due to the effect of pesticide spraying on natural enemies,considering two different kinds of impulse processes,using Hassell-Varley functional response,a predator-prey system was established in this paper.We employ the comparison theorem to get the boundedness and the sufficient condition for the permanence of predator-prey system,namely theorem 3.1 and Theorem 3.2.Finally,this paper explains the conclusion and gives the corresponding biological significance.This work provides reliable technical support for pest control in the real environment.Moreover,the method of theorem 3.2 has a wide range of applicability,and similar methods can be used to extend Hassell-Varley functional responses to other specific functional responses,such as Beddington-DeAngelies,Watt-type,Square-Root functional response and so on.The system can be used to control pests and rodents in farmland.It can also be used to protect endangered species so that predators and prey can live together to maintain ecological balance.