Abstract: Being three common nonlinear phenomena: biforcation, fractal and chaos, are there relations among them? The main objective of the present work is trying to study the issue.The typical bifurcated model (May model) and Duffing equation are studied. Using the figures of fractional dimension of time series and parameter of nonlinear system, Poincare figures, phase figures and frequency spetrum figures, it is found that the critical parameters or regions of nonlinear dynnmic system from stable state to bifucation or chaotic state can be identified effectively according to the figures of fractional-dimension-trending.