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Self-Organization in Randomly Forced Diffusion Systems: A Stochastic Sensitivity Technique

Author

Listed:
  • Alexander Kolinichenko

    (Institute of Natural Sciences and Mathematics, Ural Federal University, 620000 Ekaterinburg, Russia)

  • Irina Bashkirtseva

    (Institute of Natural Sciences and Mathematics, Ural Federal University, 620000 Ekaterinburg, Russia)

  • Lev Ryashko

    (Institute of Natural Sciences and Mathematics, Ural Federal University, 620000 Ekaterinburg, Russia)

Abstract

The problem with the analysis of noise-induced transitions between patterns in distributed stochastic systems is considered. As a key model, we use the spatially extended dynamical “phytoplankton-herbivore” system with diffusion. We perform the parametric bifurcation analysis of this model and determine the Turing instability zone, where non-homogeneous patterns are generated by diffusion. The multistability of this deterministic model with the coexistence of several waveform pattern–attractors is found. We study how noise affects these non-homogeneous patterns and estimate the dispersion of random states using a new technique based on stochastic sensitivity function (SSF) analysis and the confidence domain method. To investigate the preferences in noise-induced transitions between patterns, we analyze and compare the results of this theoretical approach with the statistics extracted from the direct numerical simulation.

Suggested Citation

  • Alexander Kolinichenko & Irina Bashkirtseva & Lev Ryashko, 2023. "Self-Organization in Randomly Forced Diffusion Systems: A Stochastic Sensitivity Technique," Mathematics, MDPI, vol. 11(2), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:451-:d:1035851
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    References listed on IDEAS

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    1. Bashkirtseva, Irina & Kolinichenko, Alexander & Ryashko, Lev, 2021. "Stochastic sensitivity of Turing patterns: methods and applications to the analysis of noise-induced transitions," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
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