Stationary Patterns of a Cross-Diffusion Prey-Predator Model with Holling Type II Functional Response
In this paper, we consider positive steady-state solutions of a cross-diffusions prey-predator model with Holling type II functional response. We investigate sufficient conditions for the existence and the nonexistence of nonconstant positive steady state solutions. It is observed that nonconstant p...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/2588998 |
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| _version_ | 1832559700004044800 |
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| author | Hongtao Zhang Jingfu Zhao |
| author_facet | Hongtao Zhang Jingfu Zhao |
| author_sort | Hongtao Zhang |
| collection | DOAJ |
| description | In this paper, we consider positive steady-state solutions of a cross-diffusions prey-predator model with Holling type II functional response. We investigate sufficient conditions for the existence and the nonexistence of nonconstant positive steady state solutions. It is observed that nonconstant positive steady states do not exist with small cross-diffusion coefficients, and the constant positive steady state is global asymptotically stable without cross-diffusion. Furthermore, we show that if natural diffusion coefficient or cross-diffusion coefficient of the predator is large enough and other diffusion coefficients are fixed, then under some conditions, at least one nonconstant positive steady state exists. |
| format | Article |
| id | doaj-art-77eb784bc27b4bb7982203ac27d30d25 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-77eb784bc27b4bb7982203ac27d30d252025-02-03T01:29:26ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/2588998Stationary Patterns of a Cross-Diffusion Prey-Predator Model with Holling Type II Functional ResponseHongtao Zhang0Jingfu Zhao1School of Mathematics and Information ScienceSchool of Mathematics and Information ScienceIn this paper, we consider positive steady-state solutions of a cross-diffusions prey-predator model with Holling type II functional response. We investigate sufficient conditions for the existence and the nonexistence of nonconstant positive steady state solutions. It is observed that nonconstant positive steady states do not exist with small cross-diffusion coefficients, and the constant positive steady state is global asymptotically stable without cross-diffusion. Furthermore, we show that if natural diffusion coefficient or cross-diffusion coefficient of the predator is large enough and other diffusion coefficients are fixed, then under some conditions, at least one nonconstant positive steady state exists.http://dx.doi.org/10.1155/2023/2588998 |
| spellingShingle | Hongtao Zhang Jingfu Zhao Stationary Patterns of a Cross-Diffusion Prey-Predator Model with Holling Type II Functional Response Journal of Mathematics |
| title | Stationary Patterns of a Cross-Diffusion Prey-Predator Model with Holling Type II Functional Response |
| title_full | Stationary Patterns of a Cross-Diffusion Prey-Predator Model with Holling Type II Functional Response |
| title_fullStr | Stationary Patterns of a Cross-Diffusion Prey-Predator Model with Holling Type II Functional Response |
| title_full_unstemmed | Stationary Patterns of a Cross-Diffusion Prey-Predator Model with Holling Type II Functional Response |
| title_short | Stationary Patterns of a Cross-Diffusion Prey-Predator Model with Holling Type II Functional Response |
| title_sort | stationary patterns of a cross diffusion prey predator model with holling type ii functional response |
| url | http://dx.doi.org/10.1155/2023/2588998 |
| work_keys_str_mv | AT hongtaozhang stationarypatternsofacrossdiffusionpreypredatormodelwithhollingtypeiifunctionalresponse AT jingfuzhao stationarypatternsofacrossdiffusionpreypredatormodelwithhollingtypeiifunctionalresponse |