Pattern formation with jump discontinuity in a predator–prey model with Holling-II functional response
This paper is focused on the existence and uniqueness of nonconstant steady states in a reaction–diffusion–ODE system, which models the predator–prey interaction with Holling-II functional response. Firstly, we aim to study the occurrence of regular stationary solutions through the application of bi...
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| Format: | Article |
| Language: | English |
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Cambridge University Press
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| Series: | European Journal of Applied Mathematics |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S0956792525000063/type/journal_article |
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| _version_ | 1849732102039273472 |
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| author | Gaihui Guo Xiaoyi Yang Conghui Zhang Shanbing Li |
| author_facet | Gaihui Guo Xiaoyi Yang Conghui Zhang Shanbing Li |
| author_sort | Gaihui Guo |
| collection | DOAJ |
| description | This paper is focused on the existence and uniqueness of nonconstant steady states in a reaction–diffusion–ODE system, which models the predator–prey interaction with Holling-II functional response. Firstly, we aim to study the occurrence of regular stationary solutions through the application of bifurcation theory. Subsequently, by a generalized mountain pass lemma, we successfully demonstrate the existence of steady states with jump discontinuity. Furthermore, the structure of stationary solutions within a one-dimensional domain is investigated and a variety of steady-state solutions are built, which may exhibit monotonicity or symmetry. In the end, we create heterogeneous equilibrium states close to a constant equilibrium state using bifurcation theory and examine their stability. |
| format | Article |
| id | doaj-art-bb6576d2a69b48fda40cb141ad1f8ef4 |
| institution | DOAJ |
| issn | 0956-7925 1469-4425 |
| language | English |
| publisher | Cambridge University Press |
| record_format | Article |
| series | European Journal of Applied Mathematics |
| spelling | doaj-art-bb6576d2a69b48fda40cb141ad1f8ef42025-08-20T03:08:20ZengCambridge University PressEuropean Journal of Applied Mathematics0956-79251469-442512310.1017/S0956792525000063Pattern formation with jump discontinuity in a predator–prey model with Holling-II functional responseGaihui Guo0Xiaoyi Yang1Conghui Zhang2Shanbing Li3School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi’an, ChinaSchool of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi’an, ChinaSchool of Science, Beijing University of Civil Engineering and Architecture, Beijing, ChinaSchool of Mathematics and Statistics, Xidian University, Xian, ChinaThis paper is focused on the existence and uniqueness of nonconstant steady states in a reaction–diffusion–ODE system, which models the predator–prey interaction with Holling-II functional response. Firstly, we aim to study the occurrence of regular stationary solutions through the application of bifurcation theory. Subsequently, by a generalized mountain pass lemma, we successfully demonstrate the existence of steady states with jump discontinuity. Furthermore, the structure of stationary solutions within a one-dimensional domain is investigated and a variety of steady-state solutions are built, which may exhibit monotonicity or symmetry. In the end, we create heterogeneous equilibrium states close to a constant equilibrium state using bifurcation theory and examine their stability.https://www.cambridge.org/core/product/identifier/S0956792525000063/type/journal_articleReaction–diffusion–ODE systempattern formationstationary solutionsstabilityjump discontinuity35B3635K5735B3535J25 |
| spellingShingle | Gaihui Guo Xiaoyi Yang Conghui Zhang Shanbing Li Pattern formation with jump discontinuity in a predator–prey model with Holling-II functional response European Journal of Applied Mathematics Reaction–diffusion–ODE system pattern formation stationary solutions stability jump discontinuity 35B36 35K57 35B35 35J25 |
| title | Pattern formation with jump discontinuity in a predator–prey model with Holling-II functional response |
| title_full | Pattern formation with jump discontinuity in a predator–prey model with Holling-II functional response |
| title_fullStr | Pattern formation with jump discontinuity in a predator–prey model with Holling-II functional response |
| title_full_unstemmed | Pattern formation with jump discontinuity in a predator–prey model with Holling-II functional response |
| title_short | Pattern formation with jump discontinuity in a predator–prey model with Holling-II functional response |
| title_sort | pattern formation with jump discontinuity in a predator prey model with holling ii functional response |
| topic | Reaction–diffusion–ODE system pattern formation stationary solutions stability jump discontinuity 35B36 35K57 35B35 35J25 |
| url | https://www.cambridge.org/core/product/identifier/S0956792525000063/type/journal_article |
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