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中文摘要：
对含有两个时滞参数、受简谐激励作用下的van der Pol-Duffing方程进行了研究，着重研究了时滞参数对该类参数激励系统的主共振的分岔响应控制．首先采用摄动法从理论上推导出时滞动力系统的分岔响应方程。用奇异性理论得到了退化余维一分岔和余维二分岔的条件。以及Hopf分岔的存在性及发生该分岔的条件，最后用数值模拟的方法研究了时滞参数对系统分岔响应的影响．研究结果表明，适当选取时滞参数，不仅可以改变分岔响应曲线的拓扑形态。还可以改变分岔点的位置．
英文摘要：
A forced system with two time-delays, including van der Pol-Duffing types, is studied. The aim is to study the primary parametrical resonance bifurcation of this system. Perturbation method is used to obtain the bifurcation equation with time-delays. Based on the bifurcation equation, co-dimension one, co-dimension two and Hope bifurcation are discussed, and the effect of time-delays on the steady state response is analyzed by numerical methods. It is indicated that the primary resonance bifurcation can be well controlled by time-delays feedback.
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