具有sturmian结构的分形网络上蜜罐的俘获问题

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-08-10 DOI:10.1142/s0218348x23500779

Yuke Huang, Cheng Zeng, Yumei Xue

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引用次数: 0

摘要

本文研究了一些进化网络中蜜罐的平均捕获时间。我们提出了一个简单的算法框架来生成具有Sturmian结构的网络。根据Sturmian词的平衡性质和递归性质，我们用渐近表达式[Formula: see text]估计我们所提出的网络的平均捕获时间，其中[Formula: see text]是与词[Formula: see text]相关的有界表达式。接下来，我们考虑具有多个蜜罐的网络，并推广我们的基本模型。此外，我们给出了一种对称的方法来创建一系列具有Sturmian结构的网络，并且平均捕获时间满足[公式:见文]，它独立于任何单词[公式:见文]。这些方法对随机网络的研究具有一定的启发性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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 [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.

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来源期刊

Fractals-Complex Geometry Patterns and Scaling in Nature and Society 数学-数学跨学科应用

CiteScore

7.40

自引率

23.40%

发文量

319

审稿时长

>12 weeks

期刊介绍： The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality. The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.