Analysis of stochastically forced equilibria and noise-induced transitions in nonlinear discrete systems
Stochastically forced discrete dynamical systems are considered. Using first approximation systems, we study dynamics of deviations of stochastic solutions from deterministic equilibria. Necessary and sufficient conditions of the existence of stable stationary solutions of equations for mean-square...
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| Format: | Article |
| Language: | Russian |
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Institute of Computer Science
2013-08-01
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| Series: | Компьютерные исследования и моделирование |
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| Online Access: | http://crm.ics.org.ru/uploads/crmissues/crm_2013_4/13405.pdf |
| _version_ | 1811221292330778624 |
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| author | Irina Adolfovna Bashkirtseva |
| author_facet | Irina Adolfovna Bashkirtseva |
| author_sort | Irina Adolfovna Bashkirtseva |
| collection | DOAJ |
| description | Stochastically forced discrete dynamical systems are considered. Using first approximation systems, we study dynamics of deviations of stochastic solutions from deterministic equilibria. Necessary and sufficient conditions of the existence of stable stationary solutions of equations for mean-square deviations are derived. Stationary values of these mean-square deviations are used for the estimations of the dispersion of random states nearby stable equilibria and analysis of noise-induced transitions. Constructive application of the suggested technique to the analysis of various stochastic regimes in Ricker population model with Allee effect is demonstrated. |
| first_indexed | 2024-04-12T07:56:51Z |
| format | Article |
| id | doaj.art-c194e7dd6a6b46ba83ee8e6d14ff2ed2 |
| institution | Directory Open Access Journal |
| issn | 2076-7633 2077-6853 |
| language | Russian |
| last_indexed | 2024-04-12T07:56:51Z |
| publishDate | 2013-08-01 |
| publisher | Institute of Computer Science |
| record_format | Article |
| series | Компьютерные исследования и моделирование |
| spelling | doaj.art-c194e7dd6a6b46ba83ee8e6d14ff2ed22022-12-22T03:41:27ZrusInstitute of Computer ScienceКомпьютерные исследования и моделирование2076-76332077-68532013-08-015455957110.20537/2076-7633-2013-5-4-559-5712065Analysis of stochastically forced equilibria and noise-induced transitions in nonlinear discrete systemsIrina Adolfovna BashkirtsevaStochastically forced discrete dynamical systems are considered. Using first approximation systems, we study dynamics of deviations of stochastic solutions from deterministic equilibria. Necessary and sufficient conditions of the existence of stable stationary solutions of equations for mean-square deviations are derived. Stationary values of these mean-square deviations are used for the estimations of the dispersion of random states nearby stable equilibria and analysis of noise-induced transitions. Constructive application of the suggested technique to the analysis of various stochastic regimes in Ricker population model with Allee effect is demonstrated.http://crm.ics.org.ru/uploads/crmissues/crm_2013_4/13405.pdfnonlinear discrete systemsrandom disturbancesnoise-induced transitionsRicker model |
| spellingShingle | Irina Adolfovna Bashkirtseva Analysis of stochastically forced equilibria and noise-induced transitions in nonlinear discrete systems Компьютерные исследования и моделирование nonlinear discrete systems random disturbances noise-induced transitions Ricker model |
| title | Analysis of stochastically forced equilibria and noise-induced transitions in nonlinear discrete systems |
| title_full | Analysis of stochastically forced equilibria and noise-induced transitions in nonlinear discrete systems |
| title_fullStr | Analysis of stochastically forced equilibria and noise-induced transitions in nonlinear discrete systems |
| title_full_unstemmed | Analysis of stochastically forced equilibria and noise-induced transitions in nonlinear discrete systems |
| title_short | Analysis of stochastically forced equilibria and noise-induced transitions in nonlinear discrete systems |
| title_sort | analysis of stochastically forced equilibria and noise induced transitions in nonlinear discrete systems |
| topic | nonlinear discrete systems random disturbances noise-induced transitions Ricker model |
| url | http://crm.ics.org.ru/uploads/crmissues/crm_2013_4/13405.pdf |
| work_keys_str_mv | AT irinaadolfovnabashkirtseva analysisofstochasticallyforcedequilibriaandnoiseinducedtransitionsinnonlineardiscretesystems |