How Inhomogeneous Site Percolation Works on Bethe Lattices: Theory and Application
Identifieur interne : 000F79 ( Main/Exploration ); précédent : 000F78; suivant : 000F80How Inhomogeneous Site Percolation Works on Bethe Lattices: Theory and Application
Auteurs : Jingli Ren [République populaire de Chine] ; Liying Zhang [République populaire de Chine] ; Stefan Siegmund [Allemagne]Source :
- Scientific Reports [ 2045-2322 ] ; 2016.
Abstract
Inhomogeneous percolation, for its closer relationship with real-life, can be more useful and reasonable than homogeneous percolation to illustrate the critical phenomena and dynamical behaviour of complex networks. However, due to its intricacy, the theoretical framework of inhomogeneous percolation is far from being complete and many challenging problems are still open. In this paper, we first investigate inhomogeneous site percolation on Bethe Lattices with two occupation probabilities, and then extend the result to percolation with
Url:
DOI: 10.1038/srep22420
PubMed: 26926785
PubMed Central: 4772486
Affiliations:
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Le document en format XML
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<front><div type="abstract" xml:lang="en"><p id="Par1">Inhomogeneous percolation, for its closer relationship with real-life, can be more useful and reasonable than homogeneous percolation to illustrate the critical phenomena and dynamical behaviour of complex networks. However, due to its intricacy, the theoretical framework of inhomogeneous percolation is far from being complete and many challenging problems are still open. In this paper, we first investigate inhomogeneous site percolation on Bethe Lattices with two occupation probabilities, and then extend the result to percolation with <italic>m</italic>
occupation probabilities. The critical behaviour of this inhomogeneous percolation is shown clearly by formulating the percolation probability <inline-formula id="IEq1"><inline-graphic xlink:href="41598_2016_Article_BFsrep22420_IEq1_HTML.gif"></inline-graphic>
</inline-formula>
with given occupation probability <italic>p</italic>
, the critical occupation probability <inline-formula id="IEq2"><inline-graphic xlink:href="41598_2016_Article_BFsrep22420_IEq2_HTML.gif"></inline-graphic>
</inline-formula>
, and the average cluster size <inline-formula id="IEq3"><inline-graphic xlink:href="41598_2016_Article_BFsrep22420_IEq3_HTML.gif"></inline-graphic>
</inline-formula>
where <italic>p</italic>
is subject to <inline-formula id="IEq4"><inline-graphic xlink:href="41598_2016_Article_BFsrep22420_IEq4_HTML.gif"></inline-graphic>
</inline-formula>
. Moreover, using the above theory, we discuss in detail the diffusion behaviour of an infectious disease (SARS) and present specific disease-control strategies in consideration of groups with different infection probabilities.</p>
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