Pattern formation of a predator-prey model with the cost of anti-predator behaviors
We propose and analyse a reaction-diffusion-advection predator-prey model in which we assume that predators move randomly but prey avoid predation by perceiving a repulsion along predator density gradient. Based on recent experimental evidence that anti-predator behaviors alone lead to a 40% reducti...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2018-05-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018035 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590051397074944 |
|---|---|
| author | Xiaoying Wang Xingfu Zou |
| author_facet | Xiaoying Wang Xingfu Zou |
| author_sort | Xiaoying Wang |
| collection | DOAJ |
| description | We propose and analyse a reaction-diffusion-advection predator-prey model in which we assume that predators move randomly but prey avoid predation by perceiving a repulsion along predator density gradient. Based on recent experimental evidence that anti-predator behaviors alone lead to a 40% reduction on prey reproduction rate, we also incorporate the cost of anti-predator responses into the local reaction terms in the model. Sufficient and necessary conditions of spatial pattern formation are obtained for various functional responses between prey and predators. By mathematical and numerical analyses, we find that small prey sensitivity to predation risk may lead to pattern formation if the Holling type Ⅱ functional response or the Beddington-DeAngelis functional response is adopted while large cost of anti-predator behaviors homogenises the system by excluding pattern formation. However, the ratio-dependent functional response gives an opposite result where large predator-taxis may lead to pattern formation but small cost of anti-predator behaviors inhibits the emergence of spatial heterogeneous solutions. |
| format | Article |
| id | doaj-art-63edd5ffe2654e80b3f1e2cad78495af |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-63edd5ffe2654e80b3f1e2cad78495af2025-01-24T02:40:50ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-05-0115377580510.3934/mbe.2018035Pattern formation of a predator-prey model with the cost of anti-predator behaviorsXiaoying Wang0Xingfu Zou1Department of Applied Mathematics, University of Western Ontario, London, ON, Canada N6A 5B7Department of Applied Mathematics, University of Western Ontario, London, ON, Canada N6A 5B7We propose and analyse a reaction-diffusion-advection predator-prey model in which we assume that predators move randomly but prey avoid predation by perceiving a repulsion along predator density gradient. Based on recent experimental evidence that anti-predator behaviors alone lead to a 40% reduction on prey reproduction rate, we also incorporate the cost of anti-predator responses into the local reaction terms in the model. Sufficient and necessary conditions of spatial pattern formation are obtained for various functional responses between prey and predators. By mathematical and numerical analyses, we find that small prey sensitivity to predation risk may lead to pattern formation if the Holling type Ⅱ functional response or the Beddington-DeAngelis functional response is adopted while large cost of anti-predator behaviors homogenises the system by excluding pattern formation. However, the ratio-dependent functional response gives an opposite result where large predator-taxis may lead to pattern formation but small cost of anti-predator behaviors inhibits the emergence of spatial heterogeneous solutions.https://www.aimspress.com/article/doi/10.3934/mbe.2018035pattern formationstabilitypredator-prey modelanti-predator behaviorsbifurcationglobal stability |
| spellingShingle | Xiaoying Wang Xingfu Zou Pattern formation of a predator-prey model with the cost of anti-predator behaviors Mathematical Biosciences and Engineering pattern formation stability predator-prey model anti-predator behaviors bifurcation global stability |
| title | Pattern formation of a predator-prey model with the cost of anti-predator behaviors |
| title_full | Pattern formation of a predator-prey model with the cost of anti-predator behaviors |
| title_fullStr | Pattern formation of a predator-prey model with the cost of anti-predator behaviors |
| title_full_unstemmed | Pattern formation of a predator-prey model with the cost of anti-predator behaviors |
| title_short | Pattern formation of a predator-prey model with the cost of anti-predator behaviors |
| title_sort | pattern formation of a predator prey model with the cost of anti predator behaviors |
| topic | pattern formation stability predator-prey model anti-predator behaviors bifurcation global stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018035 |
| work_keys_str_mv | AT xiaoyingwang patternformationofapredatorpreymodelwiththecostofantipredatorbehaviors AT xingfuzou patternformationofapredatorpreymodelwiththecostofantipredatorbehaviors |