【作者】 杨高翔；

【导师】 舒永录；

【作者基本信息】 重庆大学 ， 应用数学， 2008， 硕士

【摘要】 本文主要借助时滞微分方程的平衡点稳定性的判定方法和Hopf分支理论探讨了时滞量大小对两类偏泛函微分方程的行波解的动力学行为的影响。2001年,Wu Jianghong[1]给出了下面时滞Frisher-Kpp方程行波解的存在性2001年Joseph W.-H. So, Xingfu Zou[2]也给出了下面时滞Nicholson’s Blowfies方程行波解的存在性当上述两个方程存在行波解u ( x ,t )= ? ( z), z = x + ct和N ( x ,t )= ? ( z), z = x +ct(其中c表示波速)时,我们分别把上述两个转化为时滞微分方程如下:这时我们借助时滞微分方程中研究平衡点稳定性的判定方法和Hopf分支理论研究了上述两类偏泛函微分方程的行波解在时滞量影响下的定性行为。我们发现时滞量大小对其行波解的定性行为有着很大的影响,当时滞量穿过某个时滞阈值τ0时,其行波解将变为周期行波解。更多还原

【Abstract】 This paper mainly discussed that delay term had impact on traveling wave solution of two partial functional differential equations employing the method of stability of equilibrium and theory of Hopf bifurcation. In 2001 years, Wu Jianhong[1] acquired the existence about the traveling wave solution of delay Fish-Kpp equation and in 2001years, Joseph W.-H. So, Xingfu Zou[2] also acquired the existence about the traveling wave solution of delay Nicholson’s Blowfies equationWhen the above two equations have traveling wave solution u ( x ,t )= ? ( z),z = x + ctand N ( x ,t )= ? ( z), z = x + ct, we can transform the above equations into delay differential equations respectively as follows:We employed method of equilibrium stability and theory of Hopf bifurcation to research the qualitative behavior of the traveling wave solution of the partial functional differential equations and found that delay term has important impact on the traveling wave solution and when delay term across a certain delay valueτ0it will become periodic traveling solution.更多还原