Eigenvector Localization and Universal Regime Transitions in Multiplex Networks: A Perturbative Approach
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918163379126272 |
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| author | Tey, Joan Hernàndez Cozzo, Emanuele |
| author_facet | Tey, Joan Hernàndez Cozzo, Emanuele |
| contents | We study the transition between layer-localized and delocalized regimes in a general contact-based contagion model on multiplex networks. Using the inverse participation ratio, we characterize how activity shifts from being confined to a single layer to spreading across the entire system. Through a first-order perturbative analysis of the leading eigenvector of the supra-contact probability matrix, we derive an analytical expression for the fictive coupling $p^*$ that marks the crossover between the two regimes. This result reproduces and explains previously observed numerical scalings and extends them to a broad class of contact-based processes beyond the Susceptible-Infected-Susceptible model. We also obtain an analytical expression for the IPR of the non-dominant layer in the localized regime, confirming its power-law dependence on the coupling with exponent $α=4$. Finally, we study the transition between non-dominant and dominant layers as a function of the intra-layer activity parameter $γ$. Our analytical findings are supported by dynamical simulations that highlight distinct susceptibility patterns across regimes. Altogether, this work provides a unified spectral framework for understanding localization and dominance transitions in multiplex contagion dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04784 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eigenvector Localization and Universal Regime Transitions in Multiplex Networks: A Perturbative Approach Tey, Joan Hernàndez Cozzo, Emanuele Physics and Society Other Condensed Matter We study the transition between layer-localized and delocalized regimes in a general contact-based contagion model on multiplex networks. Using the inverse participation ratio, we characterize how activity shifts from being confined to a single layer to spreading across the entire system. Through a first-order perturbative analysis of the leading eigenvector of the supra-contact probability matrix, we derive an analytical expression for the fictive coupling $p^*$ that marks the crossover between the two regimes. This result reproduces and explains previously observed numerical scalings and extends them to a broad class of contact-based processes beyond the Susceptible-Infected-Susceptible model. We also obtain an analytical expression for the IPR of the non-dominant layer in the localized regime, confirming its power-law dependence on the coupling with exponent $α=4$. Finally, we study the transition between non-dominant and dominant layers as a function of the intra-layer activity parameter $γ$. Our analytical findings are supported by dynamical simulations that highlight distinct susceptibility patterns across regimes. Altogether, this work provides a unified spectral framework for understanding localization and dominance transitions in multiplex contagion dynamics. |
| title | Eigenvector Localization and Universal Regime Transitions in Multiplex Networks: A Perturbative Approach |
| topic | Physics and Society Other Condensed Matter |
| url | https://arxiv.org/abs/2408.04784 |