摘要
利用改进的多尺度方法对一个电路振子模型1∶3共振附近的动力学行为进行了研究.应用该方法得到了系统的复振幅方程,进而得到一个振幅与相位解耦的三维实振幅系统,通过分析实振幅方程的平衡点个数及其稳定性,将系统共振点附近的动力学行为进行分类,发现了双稳态等动力学现象,数值模拟验证了理论结果的正确性.
The dynamical behavior near a 1∶3 resonance of an electric oscillator was investigated. By using the method of multiple scale, the complex amplitude equations of the system were obtained. Then a three dimension real amplitude system in which the amplitudes decouple from the phases was given. Ana-lyzing the number of equilibrium and its stability of the real amplitude equation, the dynamical behavior around the resonant point was classified. Some interesting dynamical phenomenon were found, for exam-ple,the bistability. Numerical simulations for justifying the theoretical analysis were also provided.
出处
《郑州大学学报（理学版）》
CAS
北大核心
2016年第3期23-27,共5页
Journal of Zhengzhou University:Natural Science Edition
基金
国家自然科学基金资助项目(11302072)
河南省科技厅资助项目(112300410194)
河南教育厅资助项目(12B120004)
郑州市科技局资助项目(20141391)
关键词
电路振子
1∶3共振
多尺度方法
分岔
electric oscillator
1∶3 resonance
the method of multiple scale
bifurcation
