Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction
The Zeldovich–Semenov model of the continuous stirred tank reactor with parametric random disturbances in temperature is considered. We study a phenomenon of noise-induced transformation of the equilibrium mode into the mixed-mode oscillatory stochastic regime with alternations between small and lar...
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| Format: | Article |
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MDPI AG
2022-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/6/960 |
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| author | Lev Ryashko Irina Bashkirtseva |
| author_facet | Lev Ryashko Irina Bashkirtseva |
| author_sort | Lev Ryashko |
| collection | DOAJ |
| description | The Zeldovich–Semenov model of the continuous stirred tank reactor with parametric random disturbances in temperature is considered. We study a phenomenon of noise-induced transformation of the equilibrium mode into the mixed-mode oscillatory stochastic regime with alternations between small and large amplitudes. In the parametric analysis of the stochastic excitement, we use the analytical method of confidence domains based on the stochastic sensitivity technique. Analyzing a mutual arrangement of the confidence ellipses and separatrices, we estimate the critical intensity of the noise that causes the excitation. The phenomena of stochastic P-bifurcations and coherence resonances are discovered and studied by probability density functions and the statistics of interspike intervals. |
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| format | Article |
| id | doaj.art-d21ec22a73ca4a6a9dcd66f3e4f563ae |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T13:25:41Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d21ec22a73ca4a6a9dcd66f3e4f563ae2023-11-30T21:24:41ZengMDPI AGMathematics2227-73902022-03-0110696010.3390/math10060960Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical ReactionLev Ryashko0Irina Bashkirtseva1Institute of Natural Sciences and Mathematics, Ural Federal University, 620000 Ekaterinburg, RussiaInstitute of Natural Sciences and Mathematics, Ural Federal University, 620000 Ekaterinburg, RussiaThe Zeldovich–Semenov model of the continuous stirred tank reactor with parametric random disturbances in temperature is considered. We study a phenomenon of noise-induced transformation of the equilibrium mode into the mixed-mode oscillatory stochastic regime with alternations between small and large amplitudes. In the parametric analysis of the stochastic excitement, we use the analytical method of confidence domains based on the stochastic sensitivity technique. Analyzing a mutual arrangement of the confidence ellipses and separatrices, we estimate the critical intensity of the noise that causes the excitation. The phenomena of stochastic P-bifurcations and coherence resonances are discovered and studied by probability density functions and the statistics of interspike intervals.https://www.mdpi.com/2227-7390/10/6/960thermochemical reactionbifurcationsrandom disturbancesstochastic sensitivityexcitementcoherence resonance |
| spellingShingle | Lev Ryashko Irina Bashkirtseva Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction Mathematics thermochemical reaction bifurcations random disturbances stochastic sensitivity excitement coherence resonance |
| title | Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction |
| title_full | Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction |
| title_fullStr | Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction |
| title_full_unstemmed | Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction |
| title_short | Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction |
| title_sort | stochastic bifurcations and excitement in the zs model of a thermochemical reaction |
| topic | thermochemical reaction bifurcations random disturbances stochastic sensitivity excitement coherence resonance |
| url | https://www.mdpi.com/2227-7390/10/6/960 |
| work_keys_str_mv | AT levryashko stochasticbifurcationsandexcitementinthezsmodelofathermochemicalreaction AT irinabashkirtseva stochasticbifurcationsandexcitementinthezsmodelofathermochemicalreaction |