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Area of Science:

  • Network science
  • Statistical physics
  • Complex systems

Background:

  • Percolation theory models processes like cascading failures and epidemic spreading on networks.
  • Standard percolation relies on short-range interactions, limiting cluster formation to nearest neighbors.
  • Cumulative merging percolation (CMP) introduces long-range interactions, enabling cluster formation between topologically distant nodes.

Purpose of the Study:

  • To generalize the Cumulative Merging Percolation (CMP) framework by exploring the functional form of cluster interaction range.
  • To investigate the resulting phase transition scenarios and emergent phenomena in generalized CMP.
  • To provide a more comprehensive model for network dynamics beyond nearest-neighbor interactions.

Main Methods:

  • Development of a generalized formulation for Cumulative Merging Percolation (CMP).
  • Analytical derivation of phase transition properties based on interaction range functions.
  • Validation of theoretical predictions through numerical simulations on networks.

Main Results:

  • The generalized CMP exhibits a richer phase transition landscape compared to previous formulations.
  • Competition between different interaction mechanisms leads to observable crossover phenomena.
  • The model accurately captures emergent network dynamics not explained by standard percolation.

Conclusions:

  • Generalized CMP offers a more flexible and powerful framework for modeling complex network processes.
  • The study highlights the significant impact of long-range interactions on network structure and dynamics.
  • This work advances the understanding of percolation phenomena and their applications in diverse scientific fields.