Random attractors for ambiguously solvable systems dissipative with respect to probability
We prove a theorem on the existence of a random attractor for a multivalued random dynamical system dissipative with respect to probability. Abstract results are used for the analysis of the qualitative behavior of solutions of a system of ordinary differential equations with continuous right-hand s...
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| Date: | 2004 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2004
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3807 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509941058502656 |
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| author | Kapustyan, O. V. Капустян, О. В. |
| author_facet | Kapustyan, O. V. Капустян, О. В. |
| author_sort | Kapustyan, O. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:11:04Z |
| description | We prove a theorem on the existence of a random attractor for a multivalued random dynamical system dissipative with respect to probability. Abstract results are used for the analysis of the qualitative behavior of solutions of a system of ordinary differential equations with continuous right-hand side perturbed by a stationary random process. In terms of the Lyapunov function, for an unperturbed system, we give sufficient conditions for the existence of a random attractor. |
| first_indexed | 2026-03-24T02:49:06Z |
| format | Article |
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| id | umjimathkievua-article-3807 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:49:06Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/c7/dbe33a740067ceceab9200f07199e5c7.pdf |
| spelling | umjimathkievua-article-38072020-03-18T20:11:04Z Random attractors for ambiguously solvable systems dissipative with respect to probability Випадкові атрактори для неоднозначно розв'язних дисипативних за ймовірністю систем Kapustyan, O. V. Капустян, О. В. We prove a theorem on the existence of a random attractor for a multivalued random dynamical system dissipative with respect to probability. Abstract results are used for the analysis of the qualitative behavior of solutions of a system of ordinary differential equations with continuous right-hand side perturbed by a stationary random process. In terms of the Lyapunov function, for an unperturbed system, we give sufficient conditions for the existence of a random attractor. Доведено теорему про існування випадкового атрактора для багатозначної випадкової динамічної системи, що є дисипативною за ймовірністю. Абстрактні результати застосовано до дослідження якісної поведінки розв'язків системи звичайних диференціальних рівнянь із неперервною правою частиною, збуреної стаціонарним випадковим процесом. У термінах функції Ляпунова для незбуреної системи наведено достатні умови існування випадкового атрактора. Institute of Mathematics, NAS of Ukraine 2004-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3807 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 7 (2004); 892–900 Український математичний журнал; Том 56 № 7 (2004); 892–900 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3807/4334 https://umj.imath.kiev.ua/index.php/umj/article/view/3807/4335 Copyright (c) 2004 Kapustyan O. V. |
| spellingShingle | Kapustyan, O. V. Капустян, О. В. Random attractors for ambiguously solvable systems dissipative with respect to probability |
| title | Random attractors for ambiguously solvable systems dissipative with respect to probability |
| title_alt | Випадкові атрактори для неоднозначно розв'язних дисипативних за ймовірністю систем |
| title_full | Random attractors for ambiguously solvable systems dissipative with respect to probability |
| title_fullStr | Random attractors for ambiguously solvable systems dissipative with respect to probability |
| title_full_unstemmed | Random attractors for ambiguously solvable systems dissipative with respect to probability |
| title_short | Random attractors for ambiguously solvable systems dissipative with respect to probability |
| title_sort | random attractors for ambiguously solvable systems dissipative with respect to probability |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3807 |
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