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

Alexander Kolinichenko, Irina Bashkirtseva () and Lev Ryashko
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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

Mathematics, 2023, vol. 11, issue 2, 1-13

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.

Keywords: self-organization; patterns; diffusion model; random disturbances; stochastic sensitivity; noise-induced transitions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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