气味干扰下带有避难所的食饵-捕食者模型分析

Analysis of Model in a Predator-Prey System with Refuge Under the Impact of Odor

建立了一类考虑避难所和捕食者气味干扰的食饵-捕食者模型,研究了避难所对在捕食者气味干扰下的食饵种群的影响,并分析了系统的动力学性态,运用Dulac-Bendixson原理证明了正平衡点的全局稳定性。分析发现:当捕食者气味干扰是一个常数时,可以有效地控制食饵及捕食者种群的数量,同时促进食饵种群加入避难所,有利于食饵种群的正常繁衍,避免因食饵种群灭绝而对捕食系统造成不良影响,并且对生态自然保护区的建立也有一定的指导作用。

The impacts of odor by predator on the prey-predator model with prey refuge are explored,in order to study how the refuge of prey affect the prey-predator model with the odor by predator,whilst the dynamic behaviors of model is investigated. Using the Dulac-Bendixson theorem,we proved the global stability of the equilibrium. We found that if the odor by predator is a constant,it can control the number of prey and predator effectively,and adding the refuge for prey is good for the multiply of predator,and it can avoid the bad effect on predator-prey system caused by the prey extinction,and also have a certain guiding role for the establishment of ecological nature protection area.