论文部分内容阅读
周期激励ｖａｎｄｅｒＰｏｌ－Ｄｕｆｉｎｇ振荡器是能够呈现混沌行为的简单二阶非自治动态系统之一。本文利用谐波平衡技术和分岔理论获得了振荡器近似基谐波幅度发Ｈｏｐｆ分岔的曲线；探讨了Ｈｏｐｆ分岔与混沌出现的关系，首次剖析了ｖａｎｄｅｒＰｏｌ－Ｄｕｆｉｎｇ振荡器的Ｈｏｐｆ分岔结果是拟周期解，且拟周期解的崩溃出现混沌；数值摸拟计算出了ｖａｎｄｅｒＰｏｌ－Ｄｕｆｉｎｇ振荡器的混沌参数区域，结果表Ｈｏｐｆ分岔比Ｍｅｌｎｉｋｏｖ方法有更高的预测精度，可有效地用于预测混沌可能出现的参数区域。
Periodic excitation The vanderPol-Dufing oscillator is one of the simple second-order nonautonomous dynamic systems that can exhibit chaotic behavior. In this paper, the curve of Hopf bifurcation of oscillator with approximate fundamental harmonic amplitude is obtained by harmonic balance technique and bifurcation theory. The relationship between Hopf bifurcation and chaos appearance is discussed. The Hopf bifurcation result of vanderPol-Dufing oscillator is first analyzed Is the quasi-periodic solution, and the chaos appears in the collapse of the quasi-periodic solution. The chaos parameters of vanderPol-Dufing oscillator are numerically simulated. The results show that Hopf bifurcation has higher prediction accuracy than Melnikov method and can be used effectively in Predict the possible parameter area of chaos.