一类捕食–食饵模型正解的存在唯一性与稳定性  

Existence,Uniqueness and Stability of Positive Solutions for a Kind of Predator-prey Model

作　　者：杨梦娜 李艳玲[1] YANG Meng-na;LI Yan-ling(School of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710119)

机构地区：[1]陕西师范大学数学与信息科学学院,西安710119

出　　处：《工程数学学报》2020年第3期281-294,共14页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(61672021).

摘　　要：本文主要研究一类具有非单调生长率的捕食食饵模型的平衡态正解问题.首先通过计算锥上紧算子的不动点指标,得到了正解存在的充分条件;其次,运用线性算子扰动理论以及拓扑度理论,讨论了参数对于正解唯一性与线性稳定性的影响;最后,通过数值模拟分别验证了在一维空间和二维空间下正解的存在性结论,也就是捕食者和食饵在一定条件下可以共存.In this paper,the positive solution of the steady-state system for the predator-prey model with a non-monotonous growth rate is studied.Firstly,through calculating the fixed point index of compact maps in cone,the sufficient conditions for the existence of any possible positive solutions are obtained.Secondly,by the perturbation theory and the topological degree theory,the influence of the parameter on the uniqueness and linear stability of positive solutions is discussed.Finally,some numerical simulations are carried out to complement the existence theorem of positive solutions in one dimension and two dimensions,respectively.That is,the predator and prey can co-exist under certain conditions.

关 键 词：捕食–食饵模型 不动点指数 唯一性 稳定性 数值模拟 

分 类 号：O175.26[理学—数学]