一类含时滞的比率依赖捕食系统正平衡点的全局稳定性分析  

Global Qualitative Analysis for Positive Equilibrium of a Ratio-Dependent Predator-Prey Model

作　　者：李亚男[1] 王玉光[2] 刘磊坡[3] LI Ya-nan WANG Yu-guang LIU Lei-po(Wanfang College of Science and Technology, Henan Polytechnic University, jiaozuo 454000, China School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China Information Engineering College, Henan University of Science and Technology, Luoyang 471023, China)

机构地区：[1]河南理工大学万方科技学院,河南焦作454000 [2]宁夏大学数学计算机学院,宁夏银川750021 [3]河南科技大学信息工程学院,河南洛阳471023

出　　处：《数学的实践与认识》2017年第10期179-183,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11501170)

摘　　要：讨论了一种食饵增长为Gilpin-Ayala型的比率依赖的食饵捕食者模型,利用第二加性复合矩阵原理证明线性化系统正轨道解的稳定性,结合系统在凸集中存在唯一的局部正平衡点,证明了正平衡点的全局渐近稳定性.结合数值模拟验证了所得结论的合理性,同时指出定理结论仅为充分条件,丰富完善了模型的动力学性质.A ratio-dependent prey-predator model with Gilpin-Ayala type was discussed, on the basis of existed results, the globally asymptotically stable of positive equilibrium got by using the second additive compound matrix method, which not showed in early articles. At last, the numerical analysis verified the result.

关 键 词：比率依赖 食饵捕食者模型 全局渐近稳定性 第二加性复合矩阵 

分 类 号：O175[理学—数学]