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Transmission of Packets on a Hierarchical Network: Avalanches, Statistics and Explosive Percolation

  • Neelima Gupte
  • Ajay Deep Kachhvah
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

We discuss transport on load bearing branching hierarchical networks which can model diverse systems which can serve as models of river networks, computer networks, respiratory networks and granular media. We study avalanche transmissions and directed percolation on these networks, and on the V lattice, i.e., the strongest realization of the lattice. We find that typical realizations of the lattice show multimodal distributions for the avalanche transmissions, and a second order transition for directed percolation. On the other hand, the V lattice shows power-law behavior for avalanche transmissions, and a first order (explosive) transition to percolation. The V lattice is thus the critical case of hierarchical networks. We note that small perturbations to the V lattice destroy the power-law behavior of the distributions, and the first order nature of the percolation. We discuss the implications of our results.

Keywords

Versus Lattice Test Weight Base Lattice Hierarchical Network Percolation Transition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of PhysicsIndian Institute of Technology, MadrasChennaiIndia
  2. 2.Nonlinear Physics DivisionInstitute for Plasma ResearchGandhinagarIndia

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