Spatial patterns for a predator-prey system with Beddington-DeAngelis functional response and fractional cross-diffusion
In this paper, we investigate a predator-prey system with fractional type cross-diffusion incorporating the Beddington-DeAngelis functional response subjected to the homogeneous Neumann boundary condition. First, by using the maximum principle and the Harnack inequality, we establish a priori estima...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023990?viewType=HTML |
| _version_ | 1797794074997030912 |
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| author | Pan Xue Cuiping Ren |
| author_facet | Pan Xue Cuiping Ren |
| author_sort | Pan Xue |
| collection | DOAJ |
| description | In this paper, we investigate a predator-prey system with fractional type cross-diffusion incorporating the Beddington-DeAngelis functional response subjected to the homogeneous Neumann boundary condition. First, by using the maximum principle and the Harnack inequality, we establish a priori estimate for the positive stationary solution. Second, we study the non-existence of non-constant positive solutions mainly by employing the energy integral method and the Poincaré inequality. Finally, we discuss the existence of non-constant positive steady states for suitable large self-diffusion $ d_2 $ or cross-diffusion $ d_4 $ by using the Leray-Schauder degree theory, and the results reveal that the diffusion $ d_2 $ and the fractional type cross-diffusion $ d_4 $ can create spatial patterns. |
| first_indexed | 2024-03-13T02:57:34Z |
| format | Article |
| id | doaj.art-669fe544975b477ea054253eb5a2d7e0 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-13T02:57:34Z |
| publishDate | 2023-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-669fe544975b477ea054253eb5a2d7e02023-06-28T01:06:47ZengAIMS PressAIMS Mathematics2473-69882023-06-0188194131942610.3934/math.2023990Spatial patterns for a predator-prey system with Beddington-DeAngelis functional response and fractional cross-diffusionPan Xue0Cuiping Ren1School of General Education, Xi'an Eurasia University, Xi'an, Shaanxi 710065, ChinaSchool of General Education, Xi'an Eurasia University, Xi'an, Shaanxi 710065, ChinaIn this paper, we investigate a predator-prey system with fractional type cross-diffusion incorporating the Beddington-DeAngelis functional response subjected to the homogeneous Neumann boundary condition. First, by using the maximum principle and the Harnack inequality, we establish a priori estimate for the positive stationary solution. Second, we study the non-existence of non-constant positive solutions mainly by employing the energy integral method and the Poincaré inequality. Finally, we discuss the existence of non-constant positive steady states for suitable large self-diffusion $ d_2 $ or cross-diffusion $ d_4 $ by using the Leray-Schauder degree theory, and the results reveal that the diffusion $ d_2 $ and the fractional type cross-diffusion $ d_4 $ can create spatial patterns. https://www.aimspress.com/article/doi/10.3934/math.2023990?viewType=HTMLfractional type cross-diffusionpredator-prey systembeddington-deangelis functional responsestationary solutionleray-schauder degree |
| spellingShingle | Pan Xue Cuiping Ren Spatial patterns for a predator-prey system with Beddington-DeAngelis functional response and fractional cross-diffusion AIMS Mathematics fractional type cross-diffusion predator-prey system beddington-deangelis functional response stationary solution leray-schauder degree |
| title | Spatial patterns for a predator-prey system with Beddington-DeAngelis functional response and fractional cross-diffusion |
| title_full | Spatial patterns for a predator-prey system with Beddington-DeAngelis functional response and fractional cross-diffusion |
| title_fullStr | Spatial patterns for a predator-prey system with Beddington-DeAngelis functional response and fractional cross-diffusion |
| title_full_unstemmed | Spatial patterns for a predator-prey system with Beddington-DeAngelis functional response and fractional cross-diffusion |
| title_short | Spatial patterns for a predator-prey system with Beddington-DeAngelis functional response and fractional cross-diffusion |
| title_sort | spatial patterns for a predator prey system with beddington deangelis functional response and fractional cross diffusion |
| topic | fractional type cross-diffusion predator-prey system beddington-deangelis functional response stationary solution leray-schauder degree |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023990?viewType=HTML |
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