| 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 |
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| 引用本文： | 阮士贵,魏俊杰,肖冬梅.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[J].南京气象学院学报,2017,9(4):381-390. |
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| 作者姓名： | 阮士贵 魏俊杰 肖冬梅 |
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| 作者单位： | 迈阿密大学 数学系, 美国佛罗里达州珊瑚墙市, 33146,哈尔滨工业大学 数学系, 哈尔滨, 150001,上海交通大学 数学科学学院, 上海, 200240 |
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| 基金项目： | 美国NSF基金（DMS-1412454）；国家自然科学基金（11371248） |
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| 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.
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| 关 键 词： | 时滞微分方程 稳定性 分支 超越方程 生物系统 |
| 收稿时间： | 2016/4/18 0:00:00 |
On the distribution of zeros of a third-degree exponential polynomial with applications to delayed biological systems |
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| RUAN Shigui,WEI Junjie and XIAO Dongmei.On the distribution of zeros of a third-degree exponential polynomial with applications to delayed biological systems[J].Journal of Nanjing Institute of Meteorology,2017,9(4):381-390. |
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| Authors: | RUAN Shigui WEI Junjie and XIAO Dongmei |
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| Affiliation: | Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA,Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China and Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China |
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| Abstract: | 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. |
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| Keywords: | delayed differential equations stability bifurcation transcendental equation biological systems |
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