It has been known for quite some time that the 1 / f dynamics play a vital role in living organisms. Recently we studied the long-range correlated dynamics of Boolean networks, and found that some networks could present the 1 / f dynamics while others couldn't. An important question is what kind of networks can generate such dynamics? In this paper, we investigate this issue based on the attractor structure of Boolean networks. We find that multiple attractor networks prefer to generate the 1 /

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... f dynamics and systems with large basin entropy tend to sustain such dynamics in a wide noise range. Models for eight real genetic networks also partially support these observations.