Cross-Diffusion-Induced Turing Instability in a Two-Prey One-Predator System
This paper focuses on a strongly coupled specific ecological system consisting of two prey species and one predator. We explore a unique positive equilibrium solution of the system that is globally asymptotically stable. Additionally, we show that this equilibrium solution remains locally linearly s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/11/2411 |
| _version_ | 1827739439336521728 |
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| author | Ying Yu Yahui Chen You Zhou |
| author_facet | Ying Yu Yahui Chen You Zhou |
| author_sort | Ying Yu |
| collection | DOAJ |
| description | This paper focuses on a strongly coupled specific ecological system consisting of two prey species and one predator. We explore a unique positive equilibrium solution of the system that is globally asymptotically stable. Additionally, we show that this equilibrium solution remains locally linearly stable, even in the presence of diffusion. This means that the system does not follow classical Turing instability. However, it becomes linearly unstable only when cross-diffusion also plays a role in the system, which is called a cross-diffusion-induced instability. The corresponding numerical simulations are also demonstrated and we obtain the spatial patterns. |
| first_indexed | 2024-03-11T03:02:46Z |
| format | Article |
| id | doaj.art-8d1a759394f647ef9051ec6dce246760 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T03:02:46Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8d1a759394f647ef9051ec6dce2467602023-11-18T08:11:41ZengMDPI AGMathematics2227-73902023-05-011111241110.3390/math11112411Cross-Diffusion-Induced Turing Instability in a Two-Prey One-Predator SystemYing Yu0Yahui Chen1You Zhou2School of Mathematical Science, Yangzhou University, Yangzhou 225002, ChinaSchool of Mathematical Science, Yangzhou University, Yangzhou 225002, ChinaSchool of Mathematical Science, Yangzhou University, Yangzhou 225002, ChinaThis paper focuses on a strongly coupled specific ecological system consisting of two prey species and one predator. We explore a unique positive equilibrium solution of the system that is globally asymptotically stable. Additionally, we show that this equilibrium solution remains locally linearly stable, even in the presence of diffusion. This means that the system does not follow classical Turing instability. However, it becomes linearly unstable only when cross-diffusion also plays a role in the system, which is called a cross-diffusion-induced instability. The corresponding numerical simulations are also demonstrated and we obtain the spatial patterns.https://www.mdpi.com/2227-7390/11/11/2411predator–prey systemcross-diffusionTuring instability |
| spellingShingle | Ying Yu Yahui Chen You Zhou Cross-Diffusion-Induced Turing Instability in a Two-Prey One-Predator System Mathematics predator–prey system cross-diffusion Turing instability |
| title | Cross-Diffusion-Induced Turing Instability in a Two-Prey One-Predator System |
| title_full | Cross-Diffusion-Induced Turing Instability in a Two-Prey One-Predator System |
| title_fullStr | Cross-Diffusion-Induced Turing Instability in a Two-Prey One-Predator System |
| title_full_unstemmed | Cross-Diffusion-Induced Turing Instability in a Two-Prey One-Predator System |
| title_short | Cross-Diffusion-Induced Turing Instability in a Two-Prey One-Predator System |
| title_sort | cross diffusion induced turing instability in a two prey one predator system |
| topic | predator–prey system cross-diffusion Turing instability |
| url | https://www.mdpi.com/2227-7390/11/11/2411 |
| work_keys_str_mv | AT yingyu crossdiffusioninducedturinginstabilityinatwopreyonepredatorsystem AT yahuichen crossdiffusioninducedturinginstabilityinatwopreyonepredatorsystem AT youzhou crossdiffusioninducedturinginstabilityinatwopreyonepredatorsystem |