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To study the impact of Arctic routes on shipping networks, this paper uses an Arctic route system (ARS) model. Based on the evolution of the ARS, an improved weighted network evolution model (the BBV model) is used to predict the evolution of shipping networks from 2017 to 2035. Then, the multiple linkage analysis method is applied to extract the significant flows in the networks, and a competition network is built. The main results are as follows: (1) Significant flows in the maritime network under the influence of the ARS show an increasing trend and then a decreasing trend during evolution process. (2) According to multiple linkage analysis, Shanghai, Busan, and Tokyo have higher positions. (3) The overall network competition decreases. (4) In terms of the competitive landscape of China's container ports, Guangzhou has the strongest domestic competitive intensity. In addition, Chinese ports that face greater competition from foreign ports are always Shanghai and Shenzhen. One implication of analysis is that due to gradual influence of the ARS, port policy makers should implement different policies at different times. The paper also shows that some ports (such as Shanghai and Ningbo) should formulate cooperation agreements to promote ports development. [ABSTRACT FROM AUTHOR]