带Ivlev反应项的捕食模型正解的存在性  

The existence of positive solutions for a predator-prey model with Ivlev functional response

作　　者：马晓丽[1] 

机构地区：[1]西安工业大学理学院,陕西西安710032

出　　处：《纺织高校基础科学学报》2011年第2期212-216,共5页Basic Sciences Journal of Textile Universities

基　　金：陕西省教育厅科学研究计划项目(09JK480);西安工业大学校长基金(XAGDXJJ0803)

摘　　要：研究一类带Ivlev反应项的捕食模型的平衡态问题,给出了正解的存在性.利用Leray-Schauder度理论,通过计算锥映射不动点指标,结合极值原理、上下解方法,得到了正解存在的充分条件.结果表明,当捕食者的生长率小于自身生长所需的临界生长率时,只要食饵的生长率大于自身生长的临界生长率,两种群就可以共存;另一方面,当捕食者的生长率大于自身生长所需的临界生长率时,只要食饵的生长率适当大,两种群同样可以共存.The steady-state problem of the predator-prey model with Ivlev functional response is studied.The existence of positive solutions is established.By means of fixed point index of compact maps in cones,combining with maximum principles and lower-upper solution methods,sufficient conditions for coexistence are obtained.The results show that if the birth rate of predator is smaller than the critical value which is required to survive in the absence of prey,two species can co-existed as long as the birth rate of prey is larger than the critical value.On the other hand,if the birth rate of predator is larger than the critical value which is required to survive in the absence of prey,and the birth rate of prey is not too small,two species can also co-existed.

关 键 词：Ivlev反应项 不动点指标 存在性 

分 类 号：O175.26[理学—数学]