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.
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