摘要
捕食-食饵系统具有普遍存在性,故得到了大量研究者的关注.长久以来,普遍认为食饵数量的减少,仅仅是由于捕食者对其进行猎杀造成的.许多事实显示,在生态系统中,食饵为躲避捕食者的猎杀,会选择较安全的地方作为庇护所.除此以外,在面对捕食者的猎杀时,食饵会产生恐惧效应.因此建立了具有庇护所和恐惧效应的模型,并研究了新模型平衡点的存在性,用微分方程定性理论研究稳定性,通过微分不等式理论,证明解的有界性,且使用Dulac准则判断极限环的存在性.最后对恐惧因素所产生的影响进行分析.
The predator-prey system is universal and has attracted a lot of attention from researchers.But for a long time,it has been generally believed that the decrease in the number of prey is only caused by the hunting of predators.A lot of facts show that the prey is to avoid predators and choose safer places as shelters in the ecosystem.In addition,in the face of hunting by predators,prey will have the fear effect.Therefore,a model is established with shelter and fear effect,the existence of the equilibrium point of the new model is studied,the stability is studied with the qualitative theory of differential equations,and the boundedness of the solution is proved through the theory of differential inequality,and use the Dulac criterion to judge the existence of limit cycles.Finally,analyzing the impact of fear factors.
作者
王慧敏
张睿
WANG Hui-min;ZHANG Rui(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)
出处
《数学的实践与认识》
2021年第11期300-305,共6页
Mathematics in Practice and Theory
基金
国家自然科学基金(11761045)。
