Hénon映射的Hopf分岔分析及PSpice电路模拟  

Hopf Bifurcation of Hénon Map Analysis and Circuit Implementation Based on PSpice

作　　者：李恩颖[1] 文桂林[1] 李光耀[1] 

机构地区：[1]湖南大学汽车车身先进设计制造国家重点实验室,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2007年第9期26-29,共4页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(10672054)

摘　　要：以3阶Hénon映射作为研究对象,应用一类分岔临界准则和投影法分别分析了Hénon映射的Hopf分岔临界值和分岔解的稳定性.并以此数学模型为依据,设计了Hénon电路,基于OrCAD/PSpice建立了相关仿真模块,成功地对Hénon映射的Hopf分岔现象进行了电路模拟.模拟结果表明:该方法可以作为研究非线性动力学现象的一种有效手段,可以有效而直观地对非线性动力学进行研究和分析.A new kind of bifurcation criterion and a projection method were implemented to obtain the critical value of Hopf bifurcation of three-order Hénon map and its corresponding stability analysis. According to mathematic model, a circuit analogue of Hopf bifurcation was constructed, and the corresponding simulation model was established with OrCAD/PSpice simulation platform. Finally, the Hopf bifurcation phenomenon of a generalized Hénon map was successfully simulated, The results in circuit implementation have indicated that the circuit is functional. It has been demonstrated that the proposed approach can be an effective and visional tool in nonlinear dynamic field.

关 键 词：HOPF分岔 HÉNON映射 模拟集成电路 电路仿真 

分 类 号：O415[理学—理论物理]