Symmetric cubic Duffing's equation can be identified to three-parameter equation by using scaling transformation. Duffing's equation with, negative linear term has a closed bifurcation region under weak periodic force, the bifurcation areas contract with increasing the linear coefficient. The equation has a set of self-similar bifurcation regions under strong periodic force. The scaling property of this regions is found and discussed in terms of a one-dimensional map, the theoretical result is in good agreement with the computational result.
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