TRAPPING PROBLEM OF HONEYPOTS ON FRACTAL NETWORKS WITH THE STURMIAN STRUCTURE

Abstract

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 [Formula: see text], where [Formula: see text] is a bounded expression related to word [Formula: see text]. 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 [Formula: see text], which is independent of any word [Formula: see text]. The generalized methods may have some illuminating effects on the study of networks with randomness.