The travelling wave of Gray-Scott systems – existence, multiplicity and stability
This article studies existence and stability of travelling wave of unstirred Gray-Scott system in biological pattern formation which models an isothermal chemical reaction $ A + 2B \rightarrow 3B $ involving two chemical species, a reactant A and an auto-catalyst B, and a linear decay $ B \rightarro...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2017-08-01
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| Series: | Journal of Biological Dynamics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/17513758.2017.1308566 |
| _version_ | 1818808488615215104 |
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| author | Yuanwei Qi Yi Zhu |
| author_facet | Yuanwei Qi Yi Zhu |
| author_sort | Yuanwei Qi |
| collection | DOAJ |
| description | This article studies existence and stability of travelling wave of unstirred Gray-Scott system in biological pattern formation which models an isothermal chemical reaction $ A + 2B \rightarrow 3B $ involving two chemical species, a reactant A and an auto-catalyst B, and a linear decay $ B \rightarrow C $ , where C is an inert product. Our result shows a new and very distinctive feature of Gray-Scott type of models in generating rich and structurally different travelling pulses than related models in the literature. In particular, the existence of multiple travelling waves which have distinctive number of local maxima is proved. Furthermore, the stability of travelling wave of the reaction–diffusion system of isothermal diffusion system $ A + 2 B \rightarrow 3 B $ , is also studied. |
| first_indexed | 2024-12-18T19:42:22Z |
| format | Article |
| id | doaj.art-3e3bfa8c0fe4485583f783fe66f3c640 |
| institution | Directory Open Access Journal |
| issn | 1751-3758 1751-3766 |
| language | English |
| last_indexed | 2024-12-18T19:42:22Z |
| publishDate | 2017-08-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Biological Dynamics |
| spelling | doaj.art-3e3bfa8c0fe4485583f783fe66f3c6402022-12-21T20:55:24ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662017-08-0111037939910.1080/17513758.2017.13085661308566The travelling wave of Gray-Scott systems – existence, multiplicity and stabilityYuanwei Qi0Yi Zhu1University of Central FloridaUniversity of Central FloridaThis article studies existence and stability of travelling wave of unstirred Gray-Scott system in biological pattern formation which models an isothermal chemical reaction $ A + 2B \rightarrow 3B $ involving two chemical species, a reactant A and an auto-catalyst B, and a linear decay $ B \rightarrow C $ , where C is an inert product. Our result shows a new and very distinctive feature of Gray-Scott type of models in generating rich and structurally different travelling pulses than related models in the literature. In particular, the existence of multiple travelling waves which have distinctive number of local maxima is proved. Furthermore, the stability of travelling wave of the reaction–diffusion system of isothermal diffusion system $ A + 2 B \rightarrow 3 B $ , is also studied.http://dx.doi.org/10.1080/17513758.2017.1308566Gray-Scott modeltravelling wavemulti-peak wavesstabilityspreading of local disturbance |
| spellingShingle | Yuanwei Qi Yi Zhu The travelling wave of Gray-Scott systems – existence, multiplicity and stability Journal of Biological Dynamics Gray-Scott model travelling wave multi-peak waves stability spreading of local disturbance |
| title | The travelling wave of Gray-Scott systems – existence, multiplicity and stability |
| title_full | The travelling wave of Gray-Scott systems – existence, multiplicity and stability |
| title_fullStr | The travelling wave of Gray-Scott systems – existence, multiplicity and stability |
| title_full_unstemmed | The travelling wave of Gray-Scott systems – existence, multiplicity and stability |
| title_short | The travelling wave of Gray-Scott systems – existence, multiplicity and stability |
| title_sort | travelling wave of gray scott systems existence multiplicity and stability |
| topic | Gray-Scott model travelling wave multi-peak waves stability spreading of local disturbance |
| url | http://dx.doi.org/10.1080/17513758.2017.1308566 |
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