Global bifurcation and structure of stationary patterns of a diffusive system of plant-herbivore interactions with toxin-determined functional responses
In this paper, a homogeneous diffusive system of plant-herbivore interactions with toxin-determined functional responses is considered. We are mainly interested in studying the existence of global steady state bifurcations of the diffusive system. In particular, we also consider the case when the bi...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-02-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2023107?viewType=HTML |
| _version_ | 1797833243202945024 |
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| author | Cunbin An |
| author_facet | Cunbin An |
| author_sort | Cunbin An |
| collection | DOAJ |
| description | In this paper, a homogeneous diffusive system of plant-herbivore interactions with toxin-determined functional responses is considered. We are mainly interested in studying the existence of global steady state bifurcations of the diffusive system. In particular, we also consider the case when the bifurcation parameter, one of the diffusion rates, tends to infinity. The corresponding system is called shadow system. By using time-mapping methods, we can show the existence of the positive non-constant steady state solutions. The results tend to describe the mechanism of the spatial pattern formations for this particular system of plant-herbivore interactions. |
| first_indexed | 2024-04-09T14:20:10Z |
| format | Article |
| id | doaj.art-f8c84e58e45b4c6f80e03c5a431ac408 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-09T14:20:10Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-f8c84e58e45b4c6f80e03c5a431ac4082023-05-05T01:29:29ZengAIMS PressElectronic Research Archive2688-15942023-02-013142095210710.3934/era.2023107Global bifurcation and structure of stationary patterns of a diffusive system of plant-herbivore interactions with toxin-determined functional responsesCunbin An0School of Mathematics and Statistics, Shanxi Datong University, Datong, Shanxi 037009, ChinaIn this paper, a homogeneous diffusive system of plant-herbivore interactions with toxin-determined functional responses is considered. We are mainly interested in studying the existence of global steady state bifurcations of the diffusive system. In particular, we also consider the case when the bifurcation parameter, one of the diffusion rates, tends to infinity. The corresponding system is called shadow system. By using time-mapping methods, we can show the existence of the positive non-constant steady state solutions. The results tend to describe the mechanism of the spatial pattern formations for this particular system of plant-herbivore interactions.https://www.aimspress.com/article/doi/10.3934/era.2023107?viewType=HTMLplant-herbivore interactionstoxin-determined functional responsessteady state bifurcationsnon-constant positive solutionsshadow system |
| spellingShingle | Cunbin An Global bifurcation and structure of stationary patterns of a diffusive system of plant-herbivore interactions with toxin-determined functional responses Electronic Research Archive plant-herbivore interactions toxin-determined functional responses steady state bifurcations non-constant positive solutions shadow system |
| title | Global bifurcation and structure of stationary patterns of a diffusive system of plant-herbivore interactions with toxin-determined functional responses |
| title_full | Global bifurcation and structure of stationary patterns of a diffusive system of plant-herbivore interactions with toxin-determined functional responses |
| title_fullStr | Global bifurcation and structure of stationary patterns of a diffusive system of plant-herbivore interactions with toxin-determined functional responses |
| title_full_unstemmed | Global bifurcation and structure of stationary patterns of a diffusive system of plant-herbivore interactions with toxin-determined functional responses |
| title_short | Global bifurcation and structure of stationary patterns of a diffusive system of plant-herbivore interactions with toxin-determined functional responses |
| title_sort | global bifurcation and structure of stationary patterns of a diffusive system of plant herbivore interactions with toxin determined functional responses |
| topic | plant-herbivore interactions toxin-determined functional responses steady state bifurcations non-constant positive solutions shadow system |
| url | https://www.aimspress.com/article/doi/10.3934/era.2023107?viewType=HTML |
| work_keys_str_mv | AT cunbinan globalbifurcationandstructureofstationarypatternsofadiffusivesystemofplantherbivoreinteractionswithtoxindeterminedfunctionalresponses |