Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes
The continuous predator-prey model is one of the main models studied in recent years. The dynamical properties of these models are so complex that it is an urgent topic to be studied. In this paper, we transformed a continuous predator-prey model with modified Leslie-Gower and Hollingtype Ⅲ schemes...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2020106?viewType=HTML |
| _version_ | 1818355627234164736 |
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| author | Yangyang Li Fengxue Zhang Xianglai Zhuo |
| author_facet | Yangyang Li Fengxue Zhang Xianglai Zhuo |
| author_sort | Yangyang Li |
| collection | DOAJ |
| description | The continuous predator-prey model is one of the main models studied in recent years. The dynamical properties of these models are so complex that it is an urgent topic to be studied. In this paper, we transformed a continuous predator-prey model with modified Leslie-Gower and Hollingtype Ⅲ schemes into a discrete mode by using Euler approximation method. The existence and stability of fixed points for this discrete model were investigated. Flip bifurcation analyses of this discrete model was carried out and corresponding bifurcation conditions were obtained. Provided with these bifurcation conditions, an example was given to carry out numerical simulations, which shows that the discrete model undergoes flip bifurcation around the stable fixed point. In addition, compared with previous studies on the continuous predator-prey model, our discrete model shows more irregular and complex dynamic characteristics. The present research can be regarded as the continuation and development of the former studies. |
| first_indexed | 2024-12-13T19:44:19Z |
| format | Article |
| id | doaj.art-c0e4d7a9ab764943979474931886731e |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-13T19:44:19Z |
| publishDate | 2020-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-c0e4d7a9ab764943979474931886731e2022-12-21T23:33:35ZengAIMS PressMathematical Biosciences and Engineering1551-00182020-01-011732003201510.3934/mbe.2020106Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemesYangyang Li0Fengxue Zhang1Xianglai Zhuo22. College of Mining and Safety Engineering, Shandong University of Science and Technology, Qingdao 266590, China2. College of Mining and Safety Engineering, Shandong University of Science and Technology, Qingdao 266590, China1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaThe continuous predator-prey model is one of the main models studied in recent years. The dynamical properties of these models are so complex that it is an urgent topic to be studied. In this paper, we transformed a continuous predator-prey model with modified Leslie-Gower and Hollingtype Ⅲ schemes into a discrete mode by using Euler approximation method. The existence and stability of fixed points for this discrete model were investigated. Flip bifurcation analyses of this discrete model was carried out and corresponding bifurcation conditions were obtained. Provided with these bifurcation conditions, an example was given to carry out numerical simulations, which shows that the discrete model undergoes flip bifurcation around the stable fixed point. In addition, compared with previous studies on the continuous predator-prey model, our discrete model shows more irregular and complex dynamic characteristics. The present research can be regarded as the continuation and development of the former studies.https://www.aimspress.com/article/doi/10.3934/mbe.2020106?viewType=HTMLflip bifurcationeuler approximation methoddiscrete predator-prey modelstabilitycenter manifold theorem |
| spellingShingle | Yangyang Li Fengxue Zhang Xianglai Zhuo Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes Mathematical Biosciences and Engineering flip bifurcation euler approximation method discrete predator-prey model stability center manifold theorem |
| title | Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes |
| title_full | Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes |
| title_fullStr | Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes |
| title_full_unstemmed | Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes |
| title_short | Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes |
| title_sort | flip bifurcation of a discrete predator prey model with modified leslie gower and holling type iii schemes |
| topic | flip bifurcation euler approximation method discrete predator-prey model stability center manifold theorem |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2020106?viewType=HTML |
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