非线性延滞扩散方程的θ法动力学性态(英文)  

Dynamics of θ method for a nonlinear reaction-diffusionmodel with delay

作　　者：刘倩倩[1,2] 张平[2] 

机构地区：[1]上海市兰田中学,上海200063 [2]上海师范大学数理学院,上海200234

出　　处：《纺织高校基础科学学报》2011年第2期165-170,共6页Basic Sciences Journal of Textile Universities

基　　金：Supported by NSF of China under Grant(11071170);Chuangxin Project of Shanghai Municipal Education Commission(11ZZ118)

摘　　要：Hutchinson方程是把延滞量、扩散量及非线性变化量融为一体的人口模型,它也是Logistic方程和Fisher方程的延伸.用θ方法求解周期边界的Hutchinson方程的不动点以及不动点的线性稳定性.在给定初始值及周期边界条件时,利用中心差分及θ方法对此方程进行整体离散,得到全离散方程组的不动点,进而研究不动点的稳定性,并通过数值例子来说明不动点的线性稳定区域与θ的关系.Hutchinson＇s equation HE,which involve diffusion and a nonlinear delayed reaction term,has been proposed as a model in population dynamics.It is a natural extension of the logistic equation and fisher＇s equation.The fixed points and the influence of the delay on the long term behavior in HE were investigated.The stability regions were obtained by the use of central differences in space and θ method in time.The result shows that the linear stability region depends on θ when HE at initial conditions and periodic boundary conditions.

关 键 词：Hutchinson's方程 线性稳定 θ法 延滞 

分 类 号：O241.82[理学—计算数学]