2024/08/08 by Tey, Joan Hernàndez, Cozzo, Emanuele
#FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Physics and Society (physics.soc-ph)
paper · doi:10.48550/arxiv.2408.04784
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.