Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model
A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both...
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| Format: | Article |
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MDPI AG
2021-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/12/1329 |
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| author | Lev Ryashko Dmitri V. Alexandrov Irina Bashkirtseva |
| author_facet | Lev Ryashko Dmitri V. Alexandrov Irina Bashkirtseva |
| author_sort | Lev Ryashko |
| collection | DOAJ |
| description | A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed. |
| first_indexed | 2024-03-10T10:35:29Z |
| format | Article |
| id | doaj.art-bb0c0fceb2344fd58be0079a93a614d4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:35:29Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-bb0c0fceb2344fd58be0079a93a614d42023-11-21T23:22:19ZengMDPI AGMathematics2227-73902021-06-01912132910.3390/math9121329Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical ModelLev Ryashko0Dmitri V. Alexandrov1Irina Bashkirtseva2Department of Theoretical and Mathematical Physics, Institute of Mathematics and Computer Sciences, Ural Federal University, 620000 Ekaterinburg, RussiaDepartment of Theoretical and Mathematical Physics, Institute of Mathematics and Computer Sciences, Ural Federal University, 620000 Ekaterinburg, RussiaDepartment of Theoretical and Mathematical Physics, Institute of Mathematics and Computer Sciences, Ural Federal University, 620000 Ekaterinburg, RussiaA problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.https://www.mdpi.com/2227-7390/9/12/1329phantom attractorstochastic disturbancesclimate–vegetation modelslow-fast dynamics |
| spellingShingle | Lev Ryashko Dmitri V. Alexandrov Irina Bashkirtseva Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model Mathematics phantom attractor stochastic disturbances climate–vegetation model slow-fast dynamics |
| title | Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model |
| title_full | Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model |
| title_fullStr | Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model |
| title_full_unstemmed | Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model |
| title_short | Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model |
| title_sort | analysis of stochastic generation and shifts of phantom attractors in a climate vegetation dynamical model |
| topic | phantom attractor stochastic disturbances climate–vegetation model slow-fast dynamics |
| url | https://www.mdpi.com/2227-7390/9/12/1329 |
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