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Reaction-diffusion Processes in Scale-free Networks

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Handbook of Large-Scale Random Networks

Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 18))

Abstract

In this chapter we provide a review of the main results recently obtained in the modeling of binary fermionic reaction-diffusion processes on scale-free networks. We show how to derive rate equations within the heterogeneous mean-field formalism, and how information can be obtained from them both for finite networks in the diffusion-limited regime and in the infinite network size lime. By means of extensive numerical simulations, we check the mean field predictions and explore other aspects of the reaction-diffusion dynamics, such as density correlations and the effects of the minimum degree or a tree-like topology.

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Author information

Authors and Affiliations

  1. Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, 08034, Barcelona, Spain

    Michele Catanzaro & Romualdo Pastor-Satorras

  2. Departament de Física Fonamental, Universitat de Barcelona, 08028, Barcelona, Spain

    Marián Boguñá

Authors
  1. Michele Catanzaro
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  2. Marián Boguñá
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  3. Romualdo Pastor-Satorras
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Editor information

Editors and Affiliations

  1. Department of Pure Mathematics & Mathematical Statistics, University of Cambridge, Centre for Mathematical Sciences, Cambridge, CB3 0WB, UK

    Béla Bollobás

  2. Dept. Mathematical Sciences, University of Memphis, Memphis, TN, 38152, USA

    Béla Bollobás  & Robert Kozma  & 

  3. Alfréd Rényi Inst. of Mathematics, Reáltanoda u. 13-15, Budapest, 1053, Hungary

    Dezső Miklós

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© 2008 János Bolyai Mathematical Society and Springer-Verlag

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Catanzaro, M., Boguñá, M., Pastor-Satorras, R. (2008). Reaction-diffusion Processes in Scale-free Networks. In: Bollobás, B., Kozma, R., Miklós, D. (eds) Handbook of Large-Scale Random Networks. Bolyai Society Mathematical Studies, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69395-6_5

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