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Exotic critical behavior of weak multiplex percolation.

G J Baxter1, R A da Costa1, S N Dorogovtsev1

  • 1Department of Physics, University of Aveiro & I3N, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal.

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We explored weak multiplex percolation in interdependent networks. A giant connected component emerges differently in 2-layer vs. 3+ layer networks, showing unique phase transitions and growth patterns.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Percolation theory studies the connectivity of random networks.
  • Multiplex networks consist of multiple layers of interconnected nodes.
  • Interdependent networks exhibit complex behaviors due to layer interactions.

Purpose of the Study:

  • To investigate the critical behavior of weak multiplex percolation in interdependent networks.
  • To analyze the emergence of a giant connected component under weak percolation rules.
  • To compare phase transitions in 2-layer versus multi-layer (3+) networks.

Main Methods:

  • Mathematical modeling of weak multiplex percolation.
  • Analysis of phase transitions and component growth.
  • Study of networks with power-law degree distributions.

Main Results:

  • In two layers, a continuous phase transition with quadratic growth above the threshold is observed.
  • In three or more layers, a discontinuous hybrid transition occurs.
  • For power-law networks, the discontinuity vanishes at specific decay exponents (e.g., γ=1.5 in 3 layers).

Conclusions:

  • Weak multiplex percolation exhibits distinct critical behaviors compared to mutually connected clusters.
  • The number of layers significantly influences the type of phase transition.
  • Network degree distribution critically affects the transition dynamics in multi-layer systems.