一类延迟微分方程的数值霍普夫分支分析  

Analysis of numerical Hopf bifurcation of a delay differential equation

作　　者：李冬松[1] 王秋宝[1] 刘明珠[1] 

机构地区：[1]哈尔滨工业大学数学系,黑龙江哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2007年第1期19-23,共5页Journal of Natural Science of Heilongjiang University

摘　　要：研究一个带有延迟的逻辑方程.通过分支分析可以发现当系统参数取一些特殊值的时候出现了霍普夫分支.证明了当参数取λ=λ+O(hp)时,产生数值霍普夫分支,这里λ是精确的霍普夫分支值,h和p分别是相应的数值方法的步长与阶.数值例子验证了所给的结论.A delay logistic equation is considered. The bifurcation analysis of the model shows that Hopf bifurcation can occur as the parameter crosses some critical values. It is shown that the numerical hopf bifurcation can occur as parameter λ = λ＊ ＋ O （h^p ）, where λ＊ is precise hopf bifurcation value, h is the step length of numerical method and p is the order. At last, some numerical tests are made to verify our above conclusion.

关 键 词：逻辑方程 霍普夫分支 延迟微分方程 

分 类 号：O211.63[理学—概率论与数理统计]