一类三次超越多项式零点的分布及其在时滞生物系统的应用  

On the distribution of zeros of a third-degree exponential polynomial with applications to delayed biological systems

作　　者：阮士贵[1] 魏俊杰[2] 肖冬梅[3] RUAN Shigui WEI Junjie XIAO Dongmei(Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China)

机构地区：[1]迈阿密大学数学系,美国佛罗里达州珊瑚墙市33146 [2]哈尔滨工业大学数学系,哈尔滨150001 [3]上海交通大学数学科学学院,上海200240

出　　处：《南京信息工程大学学报（自然科学版）》2017年第4期381-390,共10页Journal of Nanjing University of Information Science & Technology（Natural Science Edition）

基　　金：美国NSF基金(DMS-1412454);国家自然科学基金(11371248)

摘　　要：本文讨论了一类三次超越多项式零点的分布,给出了零点分布在左半复平面、穿过虚轴和进入右半复平面的充分条件.作为应用,考虑了带时滞的三种群食物链模型、带时滞的睾酮分泌模型、带时滞的HIV体内感染动力学模型、带时滞的葡萄糖-胰岛素模型、带时滞的肿瘤-免疫系统作用模型的稳定性和分支问题.We consider the distribution of roots to a general third-order exponential polynomial equation and give detailed conditions about when all roots lie on the left half plane,a pair of roots cross the imaginary axis and enter the right half plane.These results can be used to discuss the local stability and Hopf bifurcation of three-dimensional biological systems with delay. We apply our results to the three-species delayed food chain models,delayed models for the control of testosterone secretion,delayed models of within-host HIV infection of CD4＋T-cells,glucose-insulin systems with delay,and tumor-immune system interaction models with delay.

关 键 词：时滞微分方程 稳定性 分支 超越方程 生物系统 

分 类 号：O175.1[理学—数学]