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Absorbing phase transition in a unidirectionally coupled layered network.

Manoj C Warambhe1, Ankosh D Deshmukh1, Prashant M Gade1

  • 1Department of Physics, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440033, India.

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Summary
This summary is machine-generated.

We investigated the contact process on layered networks, finding critical infection probability is uniform across layers. The order parameter decay differs based on network topology, with layered Erdös-Rényi networks showing hierarchical behavior.

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Area of Science:

  • Statistical Physics
  • Network Science
  • Complex Systems

Background:

  • The contact process is a fundamental model for epidemic spread and other dynamic processes on networks.
  • Layered networks, with unidirectional couplings, introduce complex spatial and temporal dependencies.
  • Understanding absorbing phase transitions in such systems is crucial for diverse applications.

Purpose of the Study:

  • To analyze the behavior of the contact process on unidirectionally coupled layered networks.
  • To investigate the critical infection probability and order parameter dynamics across different network topologies within layers.
  • To explore the influence of layer coupling on absorbing phase transitions.

Main Methods:

  • Simulation of the contact process on layered Erdös-Rényi networks and d-dimensional lattices.
  • Analysis of the order parameter decay at the critical infection probability (p_c).
  • Application of a hierarchy of differential equations within the mean-field approximation for theoretical insights.

Main Results:

  • The critical infection probability (p_c) remains constant across all layers, irrespective of topology.
  • For Erdös-Rényi layers, the order parameter decays as t^{-δ_{l}} with δ_{l}∼2^{1-l}, explained by mean-field theory.
  • A stretched exponential decay of the order parameter is observed for d-dimensional lattice layers (except the top layer).

Conclusions:

  • Layered network structure leads to universal critical behavior in terms of p_c, but distinct dynamical exponents.
  • The hierarchical coupling significantly influences the relaxation dynamics, particularly on lattice structures.
  • Mean-field approximations provide valuable insights into the observed decay patterns on Erdös-Rényi layers.