一阶延迟微分方程θ-方法的数值Hopf分支  

Numerical Hopf Bifurcation for θ-method in First Order Delay Differential Equations

作　　者：马剑[1] 张春蕊[1] 伍国兴[1] 

机构地区：[1]东北林业大学,哈尔滨150040

出　　处：《东北林业大学学报》2006年第5期115-116,共2页Journal of Northeast Forestry University

基　　金：中国博士后科学基金(2004036108)项目;东北林业大学优秀创新项目。

摘　　要：讨论了延迟微分方程的数值逼近问题,证明了当延迟微分方程经历Hopf分支时,其数值解也必定存在一个Hopf分支点,且以解析解的分支点为极限。从而阐述了方程的数值解,保持了原解析解的动力学特性。The numerical approximation algorithm for delay differential equations is discussed. It is proved that the numerical solution of a delay differential equation must have a Hopf bifurcation when the delay differential equation undergoes Hopf bifurcation, and the bifurcate point of the analytical solution is a limited point. Thereby, the numerical solution of delay differential equations was expatiated under the condition of maintaining the dynamics characteristics of the primary analytical solution.

关 键 词：延迟微分方程 Θ-方法 HOPF分支 

分 类 号：O175[理学—数学]