Positive steady-state solutions of a predator-prey system with prey-taxis
A predator-prey model with prey-taxis under homogeneous Dirichlet boundary conditions was established. Based on the prior estimate of positive solutions, the asymptotic stability of trivial and semi-trivial solutions was obtained by using the eigenvalue theory of linearization operators and spectral...
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| Format: | Article |
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Editorial Office of Journal of XPU
2024-08-01
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| Series: | Xi'an Gongcheng Daxue xuebao |
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| Online Access: | http://journal.xpu.edu.cn/en/#/digest?ArticleID=1492 |
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| _version_ | 1849727322145423360 |
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| author | DONG Yaying GAO Ge |
| author_facet | DONG Yaying GAO Ge |
| author_sort | DONG Yaying |
| collection | DOAJ |
| description | A predator-prey model with prey-taxis under homogeneous Dirichlet boundary conditions was established. Based on the prior estimate of positive solutions, the asymptotic stability of trivial and semi-trivial solutions was obtained by using the eigenvalue theory of linearization operators and spectral theory. The existence of positive steady-state solutions was established using the fixed point index theory in a cone. By analyzing two related eigenvalues, the coexistence region with respect to the growth rates of two species was obtained. The results show that prey-taxis has an obvious influence on the steady-state solutions. |
| format | Article |
| id | doaj-art-cf408a8562444ac8898d4d6cb92bfe72 |
| institution | DOAJ |
| issn | 1674-649X |
| language | zho |
| publishDate | 2024-08-01 |
| publisher | Editorial Office of Journal of XPU |
| record_format | Article |
| series | Xi'an Gongcheng Daxue xuebao |
| spelling | doaj-art-cf408a8562444ac8898d4d6cb92bfe722025-08-20T03:09:52ZzhoEditorial Office of Journal of XPUXi'an Gongcheng Daxue xuebao1674-649X2024-08-0138412213210.13338/j.issn.1674-649x.2024.04.016Positive steady-state solutions of a predator-prey system with prey-taxisDONG Yaying0GAO Ge1Scchool of Science, Xi’an Polytechnic University, Xi’an 710048, ChinaScchool of Science, Xi’an Polytechnic University, Xi’an 710048, ChinaA predator-prey model with prey-taxis under homogeneous Dirichlet boundary conditions was established. Based on the prior estimate of positive solutions, the asymptotic stability of trivial and semi-trivial solutions was obtained by using the eigenvalue theory of linearization operators and spectral theory. The existence of positive steady-state solutions was established using the fixed point index theory in a cone. By analyzing two related eigenvalues, the coexistence region with respect to the growth rates of two species was obtained. The results show that prey-taxis has an obvious influence on the steady-state solutions.http://journal.xpu.edu.cn/en/#/digest?ArticleID=1492predator-prey systemprey-taxisstabilitypositive steady-state solutions |
| spellingShingle | DONG Yaying GAO Ge Positive steady-state solutions of a predator-prey system with prey-taxis Xi'an Gongcheng Daxue xuebao predator-prey system prey-taxis stability positive steady-state solutions |
| title | Positive steady-state solutions of a predator-prey system with prey-taxis |
| title_full | Positive steady-state solutions of a predator-prey system with prey-taxis |
| title_fullStr | Positive steady-state solutions of a predator-prey system with prey-taxis |
| title_full_unstemmed | Positive steady-state solutions of a predator-prey system with prey-taxis |
| title_short | Positive steady-state solutions of a predator-prey system with prey-taxis |
| title_sort | positive steady state solutions of a predator prey system with prey taxis |
| topic | predator-prey system prey-taxis stability positive steady-state solutions |
| url | http://journal.xpu.edu.cn/en/#/digest?ArticleID=1492 |
| work_keys_str_mv | AT dongyaying positivesteadystatesolutionsofapredatorpreysystemwithpreytaxis AT gaoge positivesteadystatesolutionsofapredatorpreysystemwithpreytaxis |