Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay
In this paper, we establish a reaction-diffusion predator-prey model with weak Allee effect and delay and analyze the conditions of Turing instability. The effects of Allee effect and delay on pattern formation are discussed by numerical simulation. The results show that pattern formations change wi...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/6282958 |
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| _version_ | 1832549406773084160 |
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| author | Hua Liu Yong Ye Yumei Wei Weiyuan Ma Ming Ma Kai Zhang |
| author_facet | Hua Liu Yong Ye Yumei Wei Weiyuan Ma Ming Ma Kai Zhang |
| author_sort | Hua Liu |
| collection | DOAJ |
| description | In this paper, we establish a reaction-diffusion predator-prey model with weak Allee effect and delay and analyze the conditions of Turing instability. The effects of Allee effect and delay on pattern formation are discussed by numerical simulation. The results show that pattern formations change with the addition of weak Allee effect and delay. More specifically, as Allee effect constant and delay increases, coexistence of spotted and stripe patterns, stripe patterns, and mixture patterns emerge successively. From an ecological point of view, we find that Allee effect and delay play an important role in spatial invasion of populations. |
| format | Article |
| id | doaj-art-d119247be1764cce8f5116f29b922682 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-d119247be1764cce8f5116f29b9226822025-02-03T06:11:23ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/62829586282958Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and DelayHua Liu0Yong Ye1Yumei Wei2Weiyuan Ma3Ming Ma4Kai Zhang5School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730000, ChinaSchool of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730000, ChinaExperimental Center, Northwest Minzu University, Lanzhou 730000, ChinaSchool of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730000, ChinaSchool of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730000, ChinaSchool of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730000, ChinaIn this paper, we establish a reaction-diffusion predator-prey model with weak Allee effect and delay and analyze the conditions of Turing instability. The effects of Allee effect and delay on pattern formation are discussed by numerical simulation. The results show that pattern formations change with the addition of weak Allee effect and delay. More specifically, as Allee effect constant and delay increases, coexistence of spotted and stripe patterns, stripe patterns, and mixture patterns emerge successively. From an ecological point of view, we find that Allee effect and delay play an important role in spatial invasion of populations.http://dx.doi.org/10.1155/2019/6282958 |
| spellingShingle | Hua Liu Yong Ye Yumei Wei Weiyuan Ma Ming Ma Kai Zhang Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay Complexity |
| title | Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay |
| title_full | Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay |
| title_fullStr | Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay |
| title_full_unstemmed | Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay |
| title_short | Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay |
| title_sort | pattern formation in a reaction diffusion predator prey model with weak allee effect and delay |
| url | http://dx.doi.org/10.1155/2019/6282958 |
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