Self-oscillations in a certain Belousov–Zhabotinsky model
We consider the dynamic properties of a system of three differential equations known as the oreganator model. This model depends on four external parameters and describes one of the periodic Belousov–Zhabotinsky reactions. We obtain broad conditions for the parameters that ensure the existence of no...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2022-01-01
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| Series: | MATEC Web of Conferences |
| Online Access: | https://www.matec-conferences.org/articles/matecconf/pdf/2022/09/matecconf_cmmass2021_01011.pdf |
| _version_ | 1818017345881243648 |
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| author | Kondratieva Liudmila Romanov Aleksandr |
| author_facet | Kondratieva Liudmila Romanov Aleksandr |
| author_sort | Kondratieva Liudmila |
| collection | DOAJ |
| description | We consider the dynamic properties of a system of three differential equations known as the oreganator model. This model depends on four external parameters and describes one of the periodic Belousov–Zhabotinsky reactions. We obtain broad conditions for the parameters that ensure the existence of nonstationary steady-state regimes in oregonator model. With classical values of the parameters, the localization of the limit (at a long time) dynamics in the phase space has been improved. In fact, using numerical analysis, we significantly narrow the bounded region of the phase space containing the trajectories of the system. An iterative procedure is proposed for the approximate localization of closed trajectories (cycles) of the system on algebraic surfaces in R3. A promising problem of theoretical substantiation of the numerical convergence of this procedure is posed. |
| first_indexed | 2024-04-14T07:25:53Z |
| format | Article |
| id | doaj.art-d1e89463765249948534ddd3e98e76bd |
| institution | Directory Open Access Journal |
| issn | 2261-236X |
| language | English |
| last_indexed | 2024-04-14T07:25:53Z |
| publishDate | 2022-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | MATEC Web of Conferences |
| spelling | doaj.art-d1e89463765249948534ddd3e98e76bd2022-12-22T02:06:01ZengEDP SciencesMATEC Web of Conferences2261-236X2022-01-013620101110.1051/matecconf/202236201011matecconf_cmmass2021_01011Self-oscillations in a certain Belousov–Zhabotinsky modelKondratieva Liudmila0Romanov Aleksandr1Moscow Aviation Institute (National Research University)School of Applied Mathematics, HSE UniversityWe consider the dynamic properties of a system of three differential equations known as the oreganator model. This model depends on four external parameters and describes one of the periodic Belousov–Zhabotinsky reactions. We obtain broad conditions for the parameters that ensure the existence of nonstationary steady-state regimes in oregonator model. With classical values of the parameters, the localization of the limit (at a long time) dynamics in the phase space has been improved. In fact, using numerical analysis, we significantly narrow the bounded region of the phase space containing the trajectories of the system. An iterative procedure is proposed for the approximate localization of closed trajectories (cycles) of the system on algebraic surfaces in R3. A promising problem of theoretical substantiation of the numerical convergence of this procedure is posed.https://www.matec-conferences.org/articles/matecconf/pdf/2022/09/matecconf_cmmass2021_01011.pdf |
| spellingShingle | Kondratieva Liudmila Romanov Aleksandr Self-oscillations in a certain Belousov–Zhabotinsky model MATEC Web of Conferences |
| title | Self-oscillations in a certain Belousov–Zhabotinsky model |
| title_full | Self-oscillations in a certain Belousov–Zhabotinsky model |
| title_fullStr | Self-oscillations in a certain Belousov–Zhabotinsky model |
| title_full_unstemmed | Self-oscillations in a certain Belousov–Zhabotinsky model |
| title_short | Self-oscillations in a certain Belousov–Zhabotinsky model |
| title_sort | self oscillations in a certain belousov zhabotinsky model |
| url | https://www.matec-conferences.org/articles/matecconf/pdf/2022/09/matecconf_cmmass2021_01011.pdf |
| work_keys_str_mv | AT kondratievaliudmila selfoscillationsinacertainbelousovzhabotinskymodel AT romanovaleksandr selfoscillationsinacertainbelousovzhabotinskymodel |