Stability and Hopf Bifurcation Analysis on a Numerical Discretization of the Distributed Delay Equation  

作　　者：WU Jie ZHAN Xi-Sheng ZHANG Xian-He GAO Hong-Liang 吴杰;詹习生;张先鹤;高红亮(College of Mechatronics and Control Engineering,Hubei Normal University,Huangshi 435002)

机构地区：[1]College of Mechatronics and Control Engineering,Hubei Normal University,Huangshi 435002

出　　处：《Chinese Physics Letters》2012年第5期7-10,共4页中国物理快报（英文版）

基　　金：Supported by the National Natural Science Foundation of China under Grant Nos 61100076 and 60973012;the Foundation of Department of Education of Hubei Province under Grant D20102504.

摘　　要：A kind of discrete logistic model with distributed delays obtained by the Euler method is investigated,where the discrete delay Τ is regarded as a parameter.By analyzing the associated characteristic equation,it is found that the stability of the positive equilibrium and Hopf occurs when Τ crosses some critical value.Then the explicit formulae which determine the stability,direction and other properties of the bifurcating periodic solution are derived by using the theory of normal form and center manifold.Finally,numerical simulations are performed to verify and illustrate the analytical results.

关 键 词：parameter. value. HOPF 

分 类 号：O17[理学—数学]