TRAPPING PROBLEM of HONEYPOTS on FRACTAL NETWORKS with the STURMIAN STRUCTURE

This paper studies the average trapping time of honeypots on some evolving networks. We propose a simple algorithmic framework for generating networks with Sturmian structure. From the balance property and the recurrence property of Sturmian words, we estimate the average trapping time of our proposed networks with an asymptotic expression (T)t ∼ Mt(α)2t, where Mt(α) is a bounded expression related to word α {0, 1}∞. We next consider networks with multi-honeypots and generalize our basic models. Additionally, we give an symmetrical method to create a series of networks with the Sturmian structure, and the average trapping time satisfies (T)t ∼ 5 × 2t, which is independent of any word α. The generalized methods may have some illuminating effects on the study of networks with randomness.