History-dependent percolation on multiplex networks

Abstract

The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic. Although various critical phenomena have been found in different models, the study on the connections between different percolation transitions is still lacking. Here we propose a unified framework to study the origins of the discontinuous transitions of the percolation process on interacting networks. The model evolves in generations with the result of the present percolation depending on the previous state and thus is history-dependent. Both theoretical analysis and Monte Carlo simulations reveal that the nature of the transition remains the same at finite generations but exhibits an abrupt change for the infinite generation. We use brain functional correlation and morphological similarity data to show that our model also provides a general method to explore the network structure and can contribute to many practical applications, such as detecting the abnormal structures of human brain networks.

arXiv comment22 pages, 13 figures

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Cited by in corpus (7)

• Percolation on complex networks: Theory and application
• Efficient network immunization under limited knowledge
• Identifying vital nodes by Achlioptas process
• Explosive percolation in finite dimensions
• History-dependent percolation in two dimensions
• Iterative Site Percolation on Triangular Lattice
• Critical behaviors of cascading dynamics on multiplex two-dimensional lattices