Self-Organization in Randomly Forced Diffusion Systems: A Stochastic Sensitivity Technique
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 deter...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/2/451 |
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| author | Alexander Kolinichenko Irina Bashkirtseva Lev Ryashko |
| author_facet | Alexander Kolinichenko Irina Bashkirtseva Lev Ryashko |
| author_sort | Alexander Kolinichenko |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T11:45:48Z |
| format | Article |
| id | doaj.art-bbf414dfdfeb43f58c44921629a7ffb5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:45:48Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-bbf414dfdfeb43f58c44921629a7ffb52023-11-30T23:22:24ZengMDPI AGMathematics2227-73902023-01-0111245110.3390/math11020451Self-Organization in Randomly Forced Diffusion Systems: A Stochastic Sensitivity TechniqueAlexander Kolinichenko0Irina Bashkirtseva1Lev Ryashko2Institute of Natural Sciences and Mathematics, Ural Federal University, 620000 Ekaterinburg, RussiaInstitute of Natural Sciences and Mathematics, Ural Federal University, 620000 Ekaterinburg, RussiaInstitute of Natural Sciences and Mathematics, Ural Federal University, 620000 Ekaterinburg, RussiaThe 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.https://www.mdpi.com/2227-7390/11/2/451self-organizationpatternsdiffusion modelrandom disturbancesstochastic sensitivitynoise-induced transitions |
| spellingShingle | Alexander Kolinichenko Irina Bashkirtseva Lev Ryashko Self-Organization in Randomly Forced Diffusion Systems: A Stochastic Sensitivity Technique Mathematics self-organization patterns diffusion model random disturbances stochastic sensitivity noise-induced transitions |
| title | Self-Organization in Randomly Forced Diffusion Systems: A Stochastic Sensitivity Technique |
| title_full | Self-Organization in Randomly Forced Diffusion Systems: A Stochastic Sensitivity Technique |
| title_fullStr | Self-Organization in Randomly Forced Diffusion Systems: A Stochastic Sensitivity Technique |
| title_full_unstemmed | Self-Organization in Randomly Forced Diffusion Systems: A Stochastic Sensitivity Technique |
| title_short | Self-Organization in Randomly Forced Diffusion Systems: A Stochastic Sensitivity Technique |
| title_sort | self organization in randomly forced diffusion systems a stochastic sensitivity technique |
| topic | self-organization patterns diffusion model random disturbances stochastic sensitivity noise-induced transitions |
| url | https://www.mdpi.com/2227-7390/11/2/451 |
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