Bifurcation analysis in a discrete predator–prey model with herd behaviour and group defense
In this paper, we utilize the semi-discretization method to construct a discrete model from a continuous predator-prey model with herd behaviour and group defense. Specifically, some new results for the transcritical bifurcation, the period-doubling bifurcation, and the Neimark-Sacker bifurcation ar...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-06-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2023229?viewType=HTML |
| _version_ | 1797691002909097984 |
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| author | Jie Xia Xianyi Li |
| author_facet | Jie Xia Xianyi Li |
| author_sort | Jie Xia |
| collection | DOAJ |
| description | In this paper, we utilize the semi-discretization method to construct a discrete model from a continuous predator-prey model with herd behaviour and group defense. Specifically, some new results for the transcritical bifurcation, the period-doubling bifurcation, and the Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. Novelty includes a smooth transition from individual behaviour (low number of prey) to herd behaviour (large number of prey). Our results not only formulate simpler forms for the existence conditions of these bifurcations, but also clearly present the conditions for the direction and stability of the bifurcated closed orbits. Numerical simulations are also given to illustrate the existence of the derived Neimark-Sacker bifurcation. |
| first_indexed | 2024-03-12T02:07:19Z |
| format | Article |
| id | doaj.art-859f312a19284036b7ab190686356cc3 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-03-12T02:07:19Z |
| publishDate | 2023-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-859f312a19284036b7ab190686356cc32023-09-07T02:42:34ZengAIMS PressElectronic Research Archive2688-15942023-06-013184484450610.3934/era.2023229Bifurcation analysis in a discrete predator–prey model with herd behaviour and group defenseJie Xia0Xianyi Li1Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, ChinaDepartment of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, ChinaIn this paper, we utilize the semi-discretization method to construct a discrete model from a continuous predator-prey model with herd behaviour and group defense. Specifically, some new results for the transcritical bifurcation, the period-doubling bifurcation, and the Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. Novelty includes a smooth transition from individual behaviour (low number of prey) to herd behaviour (large number of prey). Our results not only formulate simpler forms for the existence conditions of these bifurcations, but also clearly present the conditions for the direction and stability of the bifurcated closed orbits. Numerical simulations are also given to illustrate the existence of the derived Neimark-Sacker bifurcation.https://www.aimspress.com/article/doi/10.3934/era.2023229?viewType=HTMLdiscrete predator-prey system with herd behaviour and group defensesemi-discretization methodtranscritical bifurcationperiod-doubling bifurcationneimark-sacker bifurcation |
| spellingShingle | Jie Xia Xianyi Li Bifurcation analysis in a discrete predator–prey model with herd behaviour and group defense Electronic Research Archive discrete predator-prey system with herd behaviour and group defense semi-discretization method transcritical bifurcation period-doubling bifurcation neimark-sacker bifurcation |
| title | Bifurcation analysis in a discrete predator–prey model with herd behaviour and group defense |
| title_full | Bifurcation analysis in a discrete predator–prey model with herd behaviour and group defense |
| title_fullStr | Bifurcation analysis in a discrete predator–prey model with herd behaviour and group defense |
| title_full_unstemmed | Bifurcation analysis in a discrete predator–prey model with herd behaviour and group defense |
| title_short | Bifurcation analysis in a discrete predator–prey model with herd behaviour and group defense |
| title_sort | bifurcation analysis in a discrete predator prey model with herd behaviour and group defense |
| topic | discrete predator-prey system with herd behaviour and group defense semi-discretization method transcritical bifurcation period-doubling bifurcation neimark-sacker bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/era.2023229?viewType=HTML |
| work_keys_str_mv | AT jiexia bifurcationanalysisinadiscretepredatorpreymodelwithherdbehaviourandgroupdefense AT xianyili bifurcationanalysisinadiscretepredatorpreymodelwithherdbehaviourandgroupdefense |