Complex Dynamical Behavior of Holling–Tanner Predator-Prey Model with Cross-Diffusion
Spatial predator-prey models have been studied by researchers for many years, because the exact distributions of the population can be well illustrated via pattern formation. In this paper, amplitude equations of a spatial Holling–Tanner predator-prey model are studied via multiple scale analysis. F...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/8238384 |
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| author | Caiyun Wang Yongyong Pei Yaqun Niu Ruiqiang He |
| author_facet | Caiyun Wang Yongyong Pei Yaqun Niu Ruiqiang He |
| author_sort | Caiyun Wang |
| collection | DOAJ |
| description | Spatial predator-prey models have been studied by researchers for many years, because the exact distributions of the population can be well illustrated via pattern formation. In this paper, amplitude equations of a spatial Holling–Tanner predator-prey model are studied via multiple scale analysis. First, by amplitude equations, we obtain the corresponding intervals in which different kinds of patterns will be onset. Additionally, we get the conclusion that pattern transitions of the predator are induced by the increasing rate of conversion into predator biomass. Specifically, pattern transitions of the predator between distinct Turing pattern structures vary in an orderly manner: from spotted patterns to stripe patterns, and finally to black-eye patterns. Moreover, it is discovered that pattern transitions of prey can be induced by cross-diffusion; that is, patterns of prey transmit from spotted patterns to stripe patterns and finally to a mixture of spot and stripe patterns. Meanwhile, it is found that both effects of cross-diffusion and interaction between the prey and predator can lead to the complicated phenomenon of dynamics in the system of biology. |
| format | Article |
| id | doaj-art-3ca65969c6bc42028eaa791ec5833c6a |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-3ca65969c6bc42028eaa791ec5833c6a2025-02-03T01:01:28ZengWileyComplexity1099-05262022-01-01202210.1155/2022/8238384Complex Dynamical Behavior of Holling–Tanner Predator-Prey Model with Cross-DiffusionCaiyun Wang0Yongyong Pei1Yaqun Niu2Ruiqiang He3Department of MathematicsThe Affiliated Foreign Language Middle School of Xinzhou Teachers UniversityDepartment of MathematicsDepartment of MathematicsSpatial predator-prey models have been studied by researchers for many years, because the exact distributions of the population can be well illustrated via pattern formation. In this paper, amplitude equations of a spatial Holling–Tanner predator-prey model are studied via multiple scale analysis. First, by amplitude equations, we obtain the corresponding intervals in which different kinds of patterns will be onset. Additionally, we get the conclusion that pattern transitions of the predator are induced by the increasing rate of conversion into predator biomass. Specifically, pattern transitions of the predator between distinct Turing pattern structures vary in an orderly manner: from spotted patterns to stripe patterns, and finally to black-eye patterns. Moreover, it is discovered that pattern transitions of prey can be induced by cross-diffusion; that is, patterns of prey transmit from spotted patterns to stripe patterns and finally to a mixture of spot and stripe patterns. Meanwhile, it is found that both effects of cross-diffusion and interaction between the prey and predator can lead to the complicated phenomenon of dynamics in the system of biology.http://dx.doi.org/10.1155/2022/8238384 |
| spellingShingle | Caiyun Wang Yongyong Pei Yaqun Niu Ruiqiang He Complex Dynamical Behavior of Holling–Tanner Predator-Prey Model with Cross-Diffusion Complexity |
| title | Complex Dynamical Behavior of Holling–Tanner Predator-Prey Model with Cross-Diffusion |
| title_full | Complex Dynamical Behavior of Holling–Tanner Predator-Prey Model with Cross-Diffusion |
| title_fullStr | Complex Dynamical Behavior of Holling–Tanner Predator-Prey Model with Cross-Diffusion |
| title_full_unstemmed | Complex Dynamical Behavior of Holling–Tanner Predator-Prey Model with Cross-Diffusion |
| title_short | Complex Dynamical Behavior of Holling–Tanner Predator-Prey Model with Cross-Diffusion |
| title_sort | complex dynamical behavior of holling tanner predator prey model with cross diffusion |
| url | http://dx.doi.org/10.1155/2022/8238384 |
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