时滞HTLV-I病毒模型的稳定性与分支分析
首发时间:2015-12-10
摘要:研究时滞HTLV-I病毒模型。从对系统线性化方程的特征方程根的分布分析入手,讨论了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规范型方法分析了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,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
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Stability and Bifurcation Analysis of the Time-delay HTLV-I Virus Model
Abstract:The mathematical model of HTLV-I with time delay is studied. 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, some numerical simulations are carried out for supporting the analytic results.
Keywords: applied mathematics stability Hopf bifurcation Hopf-zero bifurcation chaos
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