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This research focuses on nonlinear behaviors of Internet traffic the on the model of scale-free networks. Attractiveness parameter, which denotes the index with great influence on the behaviors and performance of system, is considered. It is shown that traffic exhibits the phase transition, scaling and 1/f-type in the power spectrum when the load of network increases, further, the nonlinear behaviors become more apparent with the attractiveness parameter growing . By using the maximal Lyapunov exponent analysis, we find that the traffic behaviors exhibits nontrivial chaos property when traffic load is approach to the critical point, which indicates more efficiency promoted, there are more unpredictability behaviors of network tend to appear on.