Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington–DeAngelis-type predator–prey model
Abstract In this paper, Turing patterns and steady state bifurcation of a diffusive Beddington–DeAngelis-type predator–prey model with density-dependent death rate for the predator are considered. We first investigate the stability and Turing instability of the unique positive equilibrium point for...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-05-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-019-1214-0 |
| _version_ | 1818497446159843328 |
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| author | Hongwu Xu Shengmao Fu |
| author_facet | Hongwu Xu Shengmao Fu |
| author_sort | Hongwu Xu |
| collection | DOAJ |
| description | Abstract In this paper, Turing patterns and steady state bifurcation of a diffusive Beddington–DeAngelis-type predator–prey model with density-dependent death rate for the predator are considered. We first investigate the stability and Turing instability of the unique positive equilibrium point for the model. Then the existence/nonexistence, the local/global structure of nonconstant positive steady state solutions, and the direction of the local bifurcation are established. Our results demonstrate that a Turing instability is induced by the density-dependent death rate under appropriate conditions, and both the general stationary pattern and Turing pattern can be observed as a result of diffusion. Moreover, some specific examples are presented to illustrate our analytical results. |
| first_indexed | 2024-12-10T18:45:52Z |
| format | Article |
| id | doaj.art-3db20113fa814b2799e9514cce9bc1ac |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-10T18:45:52Z |
| publishDate | 2019-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-3db20113fa814b2799e9514cce9bc1ac2022-12-22T01:37:30ZengSpringerOpenBoundary Value Problems1687-27702019-05-012019112310.1186/s13661-019-1214-0Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington–DeAngelis-type predator–prey modelHongwu Xu0Shengmao Fu1School of Mathematics and Statistics, Longdong UniversitySchool of Mathematics and Statistics, Northwest Normal UniversityAbstract In this paper, Turing patterns and steady state bifurcation of a diffusive Beddington–DeAngelis-type predator–prey model with density-dependent death rate for the predator are considered. We first investigate the stability and Turing instability of the unique positive equilibrium point for the model. Then the existence/nonexistence, the local/global structure of nonconstant positive steady state solutions, and the direction of the local bifurcation are established. Our results demonstrate that a Turing instability is induced by the density-dependent death rate under appropriate conditions, and both the general stationary pattern and Turing pattern can be observed as a result of diffusion. Moreover, some specific examples are presented to illustrate our analytical results.http://link.springer.com/article/10.1186/s13661-019-1214-0Predator–prey modelDensity-dependentTuring instabilityBifurcationSteady state |
| spellingShingle | Hongwu Xu Shengmao Fu Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington–DeAngelis-type predator–prey model Boundary Value Problems Predator–prey model Density-dependent Turing instability Bifurcation Steady state |
| title | Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington–DeAngelis-type predator–prey model |
| title_full | Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington–DeAngelis-type predator–prey model |
| title_fullStr | Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington–DeAngelis-type predator–prey model |
| title_full_unstemmed | Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington–DeAngelis-type predator–prey model |
| title_short | Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington–DeAngelis-type predator–prey model |
| title_sort | density dependent effects on turing patterns and steady state bifurcation in a beddington deangelis type predator prey model |
| topic | Predator–prey model Density-dependent Turing instability Bifurcation Steady state |
| url | http://link.springer.com/article/10.1186/s13661-019-1214-0 |
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