This paper deals with study of period-doubling bifurcation and chaotic behavior under the control of freqency. All structure of bifurcation and chaos can be shown on the V0-ω parameter plane by the method of frequency sweeping. The normal and inverse bifurcation sequences are fully symmetric. On the plane of the control parameters there is a point where the values merge to a unique value. The proposed method is simple and fast, and can be used to study the behavior of the chaotic dynamic systems. Not only can it be used to measure quantitatively the values of the convergence ratio δ and the rescaling factor α, but also to observe qualitatively some periodic windows which exists in the chaotic bands, as well as intermittent chaos. Bifurcation and chaos are the frequency response of the nonlinear systems.
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