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The linear noise approximation for reaction-diffusion systems on networks

Author

Listed:
  • Malbor Asllani
  • Tommaso Biancalani
  • Duccio Fanelli
  • Alan J. McKane

Abstract

Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays travelling waves in its deterministic limit. The role of stochastic fluctuations is investigated and shown to drive the emergence of stochastic waves beyond the region of the instability predicted from the deterministic theory. Simulations are performed to test the theoretical results and are analyzed via a generalized Fourier transform algorithm. This transform is defined using the eigenvectors of the discrete Laplacian defined on the network. A peak in the numerical power spectrum of the fluctuations is observed in quantitative agreement with the theoretical predictions. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Malbor Asllani & Tommaso Biancalani & Duccio Fanelli & Alan J. McKane, 2013. "The linear noise approximation for reaction-diffusion systems on networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(11), pages 1-10, November.
    • Handle: RePEc:spr:eurphb:v:86:y:2013:i:11:p:1-10:10.1140/epjb/e2013-40570-8
    DOI: 10.1140/epjb/e2013-40570-8
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    Cited by:

    1. Riccardo Muolo & Joseph D. O’Brien & Timoteo Carletti & Malbor Asllani, 2024. "Persistence of chimera states and the challenge for synchronization in real-world networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(1), pages 1-16, January.

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    Keywords

    Statistical and Nonlinear Physics;

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