以滞量为参数的广义Lienard方程的数值逼近  

Numerical Approximation of Generalized Lienard Equation with Delay As a Parameter

作　　者：初颖[1] 吕堂红[1] 

机构地区：[1]长春理工大学理学院,长春130022

出　　处：《长春理工大学学报（自然科学版）》2017年第5期128-131,共4页Journal of Changchun University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金(10726062)

摘　　要：利用欧拉方法研究了对以滞量为参数的具有Hopf分支的广义Lienard方程的数值逼近问题。首先,利用欧拉方法将得到的时滞差分方程表示为映射,然后以时滞r为分支参数,利用离散动力系统的分支理论,在广义Lienard方程具有Hopf分支的条件下,给出了差分方程Hopf分支存在的条件,及连续系统与其数值逼近间的关系,证明了当该系统在r=r0产生Hopf分支时,其数值逼近也在相应的参数rh处具有Hopf分支,并且rh=r0+o(h),最后给出了一个数值仿真的例子,仿真结果表明Euler离散后的系统依旧保持了原系统的动力学性质,从而验证了理论结果的正确性.The numerical approximation of the generalized Lienard equation which has Hopf bifurcations and with delay as parameter is considerd by using Euler method. Firstly, the delay deference equation obtained by using Euler method is written as a mapping. Then,under the condition that the generalized Lienard equation has Hopf bifurcation,by taking time delay r as the bifurcation parameter and using the bifurcation theory of discrete dynamical systems, we give the conditions for the existence of Hopf bifurcation of difference equations and the relationship between continuous system and numerical approximation of the continuous system, furthermore, we proved that the numerical approximation also has Hopf bifurcations at corresponding parameters rh and rh=r0＋o（h） when the system has Hopf bifurcations at r=r0 . Finally, an example of numerical simulation is given, the simulation results show that the system which is discretized by Euler till keeps the dynamical property of the original system,which verifies the correctness of the theoretical results.

关 键 词：广义LIENARD方程 欧拉方法 HOPF分支 数值逼近 

分 类 号：O175.12[理学—数学]