How Inhomogeneous Site Percolation Works on Bethe Lattices: Theory and Application
Identifieur interne : 000857 ( Main/Exploration ); précédent : 000856; suivant : 000858How Inhomogeneous Site Percolation Works on Bethe Lattices: Theory and Application
Auteurs : Jingli Ren ; Liying Zhang ; 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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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">How Inhomogeneous Site Percolation Works on Bethe Lattices: Theory and Application</title><author><name sortKey="Ren, Jingli" sort="Ren, Jingli" uniqKey="Ren J" first="Jingli" last="Ren">Jingli Ren</name><affiliation><nlm:aff id="a1"><institution>School of Mathematics and Statistics, Zhengzhou University</institution>, 450001 Zhengzhou,<country>P.R. China</country></nlm:aff><wicri:noCountry code="nlm country">P.R. China</wicri:noCountry></affiliation></author><author><name sortKey="Zhang, Liying" sort="Zhang, Liying" uniqKey="Zhang L" first="Liying" last="Zhang">Liying Zhang</name><affiliation><nlm:aff id="a1"><institution>School of Mathematics and Statistics, Zhengzhou University</institution>, 450001 Zhengzhou,<country>P.R. China</country></nlm:aff><wicri:noCountry code="nlm country">P.R. China</wicri:noCountry></affiliation></author><author><name sortKey="Siegmund, Stefan" sort="Siegmund, Stefan" uniqKey="Siegmund S" first="Stefan" last="Siegmund">Stefan Siegmund</name><affiliation wicri:level="1"><nlm:aff id="a2"><institution>Center for Dynamics & Institute for Analysis, Department of Mathematics</institution>, TU Dresden, 01062 Dresden,<country>Germany</country></nlm:aff><country xml:lang="fr">Allemagne</country><wicri:regionArea># see nlm:aff country strict</wicri:regionArea></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">26926785</idno><idno type="pmc">4772486</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4772486</idno><idno type="RBID">PMC:4772486</idno><idno type="doi">10.1038/srep22420</idno><date when="2016">2016</date><idno type="wicri:Area/Pmc/Corpus">000063</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000063</idno><idno type="wicri:Area/Pmc/Curation">000063</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Curation">000063</idno><idno type="wicri:Area/Pmc/Checkpoint">000267</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Checkpoint">000267</idno><idno type="wicri:Area/Ncbi/Merge">000528</idno><idno type="wicri:Area/Ncbi/Curation">000528</idno><idno type="wicri:Area/Ncbi/Checkpoint">000528</idno><idno type="wicri:Area/Main/Merge">000859</idno><idno type="wicri:Area/Main/Curation">000857</idno><idno type="wicri:Area/Main/Exploration">000857</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">How Inhomogeneous Site Percolation Works on Bethe Lattices: Theory and Application</title><author><name sortKey="Ren, Jingli" sort="Ren, Jingli" uniqKey="Ren J" first="Jingli" last="Ren">Jingli Ren</name><affiliation><nlm:aff id="a1"><institution>School of Mathematics and Statistics, Zhengzhou University</institution>, 450001 Zhengzhou,<country>P.R. China</country></nlm:aff><wicri:noCountry code="nlm country">P.R. China</wicri:noCountry></affiliation></author><author><name sortKey="Zhang, Liying" sort="Zhang, Liying" uniqKey="Zhang L" first="Liying" last="Zhang">Liying Zhang</name><affiliation><nlm:aff id="a1"><institution>School of Mathematics and Statistics, Zhengzhou University</institution>, 450001 Zhengzhou,<country>P.R. China</country></nlm:aff><wicri:noCountry code="nlm country">P.R. China</wicri:noCountry></affiliation></author><author><name sortKey="Siegmund, Stefan" sort="Siegmund, Stefan" uniqKey="Siegmund S" first="Stefan" last="Siegmund">Stefan Siegmund</name><affiliation wicri:level="1"><nlm:aff id="a2"><institution>Center for Dynamics & Institute for Analysis, Department of Mathematics</institution>, TU Dresden, 01062 Dresden,<country>Germany</country></nlm:aff><country xml:lang="fr">Allemagne</country><wicri:regionArea># see nlm:aff country strict</wicri:regionArea></affiliation></author></analytic><series><title level="j">Scientific Reports</title><idno type="eISSN">2045-2322</idno><imprint><date when="2016">2016</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>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="d33e321"><inline-graphic id="d33e322" xlink:href="srep22420-m1.jpg"></inline-graphic></inline-formula> with given occupation probability <italic>p</italic>, the critical occupation probability <inline-formula id="d33e327"><inline-graphic id="d33e328" xlink:href="srep22420-m2.jpg"></inline-graphic></inline-formula>, and the average cluster size <inline-formula id="d33e330"><inline-graphic id="d33e331" xlink:href="srep22420-m3.jpg"></inline-graphic></inline-formula> where <italic>p</italic> is subject to <inline-formula id="d33e337"><inline-graphic id="d33e338" xlink:href="srep22420-m4.jpg"></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></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Stauffer, D" uniqKey="Stauffer D">D. Stauffer</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Essam, J W" uniqKey="Essam J">J. W. Essam</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Grimmett, G R" uniqKey="Grimmett G">G. R. Grimmett</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ghanbarzadeh, S" uniqKey="Ghanbarzadeh S">S. Ghanbarzadeh</name></author><author><name sortKey="Prodanovi, M" uniqKey="Prodanovi M">M. Prodanović</name></author><author><name sortKey="Hesse, M A" uniqKey="Hesse M">M. A. 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