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Stochastic sensitivity of Turing patterns: methods and applications to the analysis of noise-induced transitions

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  • Bashkirtseva, Irina
  • Kolinichenko, Alexander
  • Ryashko, Lev

Abstract

In this paper, a problem of the analysis of the randomly forced patterns in spatially distributed systems with diffusion is considered. For the approximation of mean-square deviations of random solutions from the unforced deterministic pattern-attractors, we suggest a constructive method based on the stochastic sensitivity technique. To demonstrate an efficiency of this method, we consider the Levin-Segel model with formation of non-homogeneous structures of the phytoplankton and herbivore populations. The spatial peculiarities of probabilistic distributions near patterns are investigated. The dependence of the stochastic sensitivity on the variation of system parameters is studied. An application of the stochastic sensitivity technique to the study of noise-induced transitions between coexisting spatial structures is demonstrated.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008456
    DOI: 10.1016/j.chaos.2021.111491
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    References listed on IDEAS

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    1. Slepukhina, E. & Ryashko, L. & Kügler, P., 2020. "Noise-induced early afterdepolarizations in a three-dimensional cardiac action potential model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Irina Bashkirtseva & Alexander Pankratov, 2019. "Stochastic Higgins model with diffusion: pattern formation, multistability and noise-induced preference," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(10), pages 1-9, October.
    3. Marco A. Morales & Irving Fernández-Cervantes & Ricardo Agustín-Serrano & Andrés Anzo & Mercedes P. Sampedro, 2016. "Patterns formation in ferrofluids and solid dissolutions using stochastic models with dissipative dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(8), pages 1-17, August.
    4. V.O. Kharchenko & D.O. Kharchenko, 2012. "Noise-induced pattern formation in system of point defects subjected to irradiation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 85(11), pages 1-12, November.
    5. Rybalova, E.V. & Strelkova, G.I. & Anishchenko, V.S., 2021. "Impact of sparse inter-layer coupling on the dynamics of a heterogeneous multilayer network of chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    6. La Barbera, A & Spagnolo, B, 2002. "Spatio-temporal patterns in population dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 120-124.
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    Cited by:

    1. Yu, Xingwang & Ma, Yuanlin, 2022. "Steady-state analysis of the stochastic Beverton-Holt growth model driven by correlated colored noises," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. 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.

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