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时滞HTLV-I病毒模型的稳定性与分支分析

发表时间:2016-04-15  浏览量:1683  下载量:679
全部作者: 杨纪华,张二丽,刘媚
作者单位: 宁夏师范学院数学与计算机科学学院;郑州财经学院信息工程学院
摘 要: 从系统线性化方程特征方程根的分布分析入手,讨论系统平衡点的局部稳定性,确定了系统的线性稳定性区域,发现当系统中的时滞经过一系列临界值时,系统经历了Hopf分支和Hopf-zero分支,并发现当时滞较大时,系统出现了混沌现象。然后,利用中心流形理论和Hassard规范型方法分析分支周期解的稳定性和Hopf分支的分支方向,给出了关于分支方向和分支周期解稳定性的详细计算公式。最后,通过数值模拟验证了理论结果。
关 键 词: 应用数学;稳定性;Hopf分支;Hopf-zero分支;混沌
Title: Stability and bifurcation analysis of the time-delay HTLV-I
Author: YANG Jihua, ZHANG Erli, LIU Mei
Organization: School of Mathematics and Computer Science, Ningxia Normal University; School of Information Engineering, Zhengzhou Institute of Finance and Economics
Abstract: The local stability of the equilibrium is discussed by analyzing the characteristic equation of the linearized system of original system at the equilibrium. The regions of linear stability of equilibrium are given, it is found that Hopf bifurcation and Hopf-zero bifurcation exist when the delay passes through a sequence of critical values and the chaos occurs when delay increase further. Then, using the center manifold theorem and the Hassard normal form method, the explicit formulas for determining the direction and stability of the Hopf bifurcation are determined. Finally, numerical simulations are carried out for supporting the analytic results.
Key words: applied mathematics; stability; Hopf bifurcation; Hopf-zero bifurcation; chaos
发表期数: 2016年4月第7期
引用格式: 杨纪华,张二丽,刘媚. 时滞HTLV-I病毒模型的稳定性与分支分析[J]. 中国科技论文在线精品论文,2016,9(7):650-661.
 
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