一类具有Logistic增长和Holling II类功能反应的免疫模型

裴永珍, 王慧娜, 李长国, 高淑京

数学学报 ›› 2011, Vol. 54 ›› Issue (2) : 301-312.

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PDF(594 KB)
数学学报 ›› 2011, Vol. 54 ›› Issue (2) : 301-312. DOI: 10.12386/A2011sxxb0031
论文

一类具有Logistic增长和Holling II类功能反应的免疫模型

    裴永珍1, 王慧娜1, 李长国2, 高淑京3
作者信息 +

An Immune Model with Logistic Growth and Holling Type-II Functional Response

    Yong Zhen PEI1, Hui Na WANG1, Chang Guo LI2, Shu Jing GAO3
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摘要

研究了一类具有Logistic 增长和Holling II 类功能反应的免疫模型. 以时滞为分支参数, 分析了系统正平衡点的稳定性和Hopf 分支的存在性; 然后利用中心流形定理和规范型方法, 给出了分支周期解的分支方向与稳定性的计算公式, 利用数值模拟验证了所得结论.

 

Abstract

A basic model of immune with Logistic growth and Holling type-II functional response has been studied. By choosing the time delay as the parameter, the stability of the positive equilibrium and the existence of the Hopf bifurcation are investigated. By using the normal form theory and the center argument, the explicit formulae which determine the stability and the direction are derived. Finally, numerical simulations supporting our theoretical results are also included.

 

关键词

时滞 / 免疫模型 / Holling II 类功能反应

Key words

Time delay / Immune model / Holling type-II functional response

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导出引用
裴永珍, 王慧娜, 李长国, 高淑京. 一类具有Logistic增长和Holling II类功能反应的免疫模型. 数学学报, 2011, 54(2): 301-312 https://doi.org/10.12386/A2011sxxb0031
Yong Zhen PEI, Hui Na WANG, Chang Guo LI, Shu Jing GAO. An Immune Model with Logistic Growth and Holling Type-II Functional Response. Acta Mathematica Sinica, Chinese Series, 2011, 54(2): 301-312 https://doi.org/10.12386/A2011sxxb0031

参考文献


[1] Buri? N., Vasovi? N., Sufficiently general framework for simple models of the net immune response, Chaos, Solitons and Fractals, 2002, 13: 1771-1782.

[2] YuW., Cao J., Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with time delays, Physics Letters A, 2006, 351: 64-78.

[3] Zhang J., Jin Z., Yan J., Sun G., Stability and Hopf bifurcation in a delayed competition system, Nonlinear Analysis: Theory, Methods and Applications, 2009, 70: 658-670.

[4] Meng X., Han D., Song Y., Stability and Hopf Bifurcation in a non-kolmogorov type Predator-Prey with delay, Mathematical and Computer Modeling, 2005, 41: 1445-1455.

[5] Ruan S., Wei J., On the zeros of transcendental functions with applications to stability of delay differential equations with two delays, Dynamics of Continuous, Dicrete and Impulsive systems Series A: Mathematical Analysis, 2003, 10: 863-874.

[6] Hassard B., Kazarinoff N., Wan Y., Theory and Applications of Hopf Bifurcation, Cambridge: Cambridge University Press, 1981.

基金

国家自然科学基金资助项目(10971037)

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