Reaction-diffusion processes in scale-free networks

Lazaros K. Gallos, Panos Argyrakis

Research output: Contribution to journalConference articlepeer-review


In this work we investigate the dynamics of reaction-diffusion processes on scale-free networks. Particles of two types, A and B, are randomly distributed on such a network and difuse using random walk models by hopping to nearest neighbor nodes only. Here we treat the case where one species is immobile and the other is mobile. The immobile species acts as a trap, i.e. when particles of the other species encounter a trap node they are immediately annihilated. We numerically compute φ(n, c), the survival probability of mobile species at time n, as a function of the concentration of trap nodes, c. We compare our results to the mean-field result (Rosenstock approximation), and the exact result for lattices of Donsker-Varadhan. We find that for high connectivity networks and high trap concentrations the mean-field result of a simple exponential decay is also valid here. But for low connectivity networks and low c the behavior is much more complicated. We explain these trends in terms of the number of sites visited, Sn, the system size, and the concentration of traps.

Original languageEnglish (US)
Pages (from-to)118-125
Number of pages8
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - 2003
Externally publishedYes
EventNoise in Complex Systems and Stochastic Dynamics - Santa Fe, NM, United States
Duration: Jun 2 2003Jun 4 2003

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


  • Reaction-diffusion
  • Scale-free networks
  • Trapping


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