一类食饵具有Allee 效应的捕食-食饵模型的分歧解  

Bifurcation Solution of a Diffusive Predator-prey Model with Allee Effect in Prey

作　　者：曹倩 李艳玲[2] CAO Qian;LI Yan-ling(School of Science,Chang'an University,Xi'an 710064;College of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710119)

机构地区：[1]长安大学理学院,西安710064 [2]陕西师范大学数学与统计学院,西安710119

出　　处：《工程数学学报》2021年第3期377-388,共12页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(61672021);中央高校基本科研业务费专项资金(300102120103)。

摘　　要：在种群生态学中,Allee效应普遍存在,且研究Allee效应对种群的生存和发展至关重要.本文研究一类食饵具有双Allee效应的捕食-食饵模型的分歧解.首先,利用稳定性理论证明常数解的稳定性.其次,以食饵的扩散系数为分歧参数,用局部分歧定理分别研究强Allee效应和弱Allee效应两种情况下发自正常数解的局部分歧解,因此得到共存解存在性的充分条件.最后,利用数值模拟直观呈现理论分析的结果.结果表明,当捕食者的死亡率、扩散率、捕食率满足一定条件时,捕食者和食饵在强Allee效应和弱Allee效应的情形下都可以共存.Allee effect is very common in population ecology.It is very important to study Allee effect for the survival and development of population.Therefore,we consider the bifurcation solutions of a diffusive predator-prey model with double Allee effect in prey.Firstly,we analyze the stability of constant solutions by stability theory.Secondly,by taking the diffusion coefficient of prey as the bifurcation parameter,we investigate that the local bifurcation solutions evolve from a positive constant solution under strong Allee effect and weak Allee effect,respectively,by local bifurcation theory,which gives a sufficient condition for the existence of coexistence solutions.Finally,we visually present theoretical results by numerical simulation.The results show that the predator and prey can coexist under strong Allee effect or weak Allee effect when the death rate,diffusion rate and predation rate of the predator satisfy certain conditions.

关 键 词：双Allee效应 捕食-食饵模型 分歧解 稳定性 

分 类 号：O175.26[理学—数学]