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This research aims to analyze how breakdown probabilities in Sierpinski-type networks influence stationary electron distributions.

April 14, 2026Fractals0 citations

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The Kullback-Leibler divergence of the Sierpinski-type networks

YHYuke HuangBeijing University of Posts and Telecommunications HZHanxiong ZhangChina University of Mining and Technology CZCheng Zeng

Key Points

This research aims to analyze how breakdown probabilities in Sierpinski-type networks influence stationary electron distributions.
Introduced a fractal network based on the Sierpinski antenna.
Applied random walk theory to model electron movement across different layers.
Used the Kullback-Leibler divergence to quantify differences in stationary distributions.
Investigated two random models: Bernoulli and Erdös-Rènyi.
Different breakdown probabilities significantly alter the stationary distribution of electrons.
Kullback-Leibler divergence reveals specific patterns in electron distribution changes across models.
Findings suggest applicability of the model to fields like cyberspace security.

Abstract

In this paper, we introduce a type of fractal networks generated by the Sierpinski fractal antenna. The electrons shuttle through the piece of antenna in different layers via random walk, and also break down the adjacent pieces in the same layer with probability Formula: see text. Different breakdown probabilities will affect the stationary distribution of electrons in the hierarchical network. We use the Kullback-Leibler divergence (KLD, relative entropy) to study this effect. We consider two kinds of random models: the Bernoulli model and the Erdös-Rènyi model. It makes our research also applicable to some other fields, such as cyberspace security.

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The Kullback-Leibler divergence of the Sierpinski-type networks

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