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分形、分岔和混沌作为三种常见的非线性现象，它们之间是否存在什么联系？为了探索此问题，本文通过对一经典倍周期分岔模型─—Ｍａｙ模型及ＤＵｆｆｉｎｇ方程的研究，得出利用随参数变化的时间序列分维数图，可以很好地识别非线性模型从确定性状态到分岔或混沌状态的临界参数点或区域。
Fractal, bifurcation and chaos as three common non-linear phenomena, whether there is any relationship between them? In order to explore this problem, this paper studies the classic double-period bifurcation model-May model and the DUffing equation, and draws the conclusion that using the time-series fractal dimension diagrams that change with the parameters can well identify the nonlinear model from deterministic State to critical point or region of bifurcation or chaos.