Influence of Allee effect in prey populations on the dynamics of two-prey-one-predator model
One of the important ecological challenges is to capture the complex dynamics and understand the underlying regulating ecological factors. Allee effect is one of the important factors in ecology and taking it into account can cause significant changes to the system dynamics. In this work we consider...
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AIMS Press
2018-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018040 |
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| author | Moitri Sen Malay Banerjee Yasuhiro Takeuchi |
| author_facet | Moitri Sen Malay Banerjee Yasuhiro Takeuchi |
| author_sort | Moitri Sen |
| collection | DOAJ |
| description | One of the important ecological challenges is to capture the complex dynamics and understand the underlying regulating ecological factors. Allee effect is one of the important factors in ecology and taking it into account can cause significant changes to the system dynamics. In this work we consider a two prey-one predator model where the growth of both the prey population is subjected to Allee effect, and the predator is generalist as it survives on both the prey populations. We analyze the role of Allee effect on the dynamics of the system, knowing the dynamics of the model without Allee effect. Interestingly we have observed through a comprehensive bifurcation study that incorporation of Allee effect enriches the local as well as the global dynamics of the system. Specially after a certain threshold value of the Allee effect, it has a very significant effect on the chaotic dynamics of the system. In course of the bifurcation analysis we have explored all possible bifurcations such as the existence of transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and Bautin bifurcation and period-doubling route to chaos respectively. |
| format | Article |
| id | doaj-art-1f2c4aa9ff364d3381bcbbc18dd201e6 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-1f2c4aa9ff364d3381bcbbc18dd201e62025-01-24T02:40:56ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-07-0115488390410.3934/mbe.2018040Influence of Allee effect in prey populations on the dynamics of two-prey-one-predator modelMoitri Sen0Malay Banerjee1Yasuhiro Takeuchi2Department of Mathematics, National Institute of Technology, Patna, Bihar-800005, IndiaDepartment of Mathematics & Statistics, Indian Institute of Technology Kanpur, Uttar Pradesh-208016, IndiaDepartment of Physics and Mathematics, Aoyama Gakuin University, Kanagawa, JapanOne of the important ecological challenges is to capture the complex dynamics and understand the underlying regulating ecological factors. Allee effect is one of the important factors in ecology and taking it into account can cause significant changes to the system dynamics. In this work we consider a two prey-one predator model where the growth of both the prey population is subjected to Allee effect, and the predator is generalist as it survives on both the prey populations. We analyze the role of Allee effect on the dynamics of the system, knowing the dynamics of the model without Allee effect. Interestingly we have observed through a comprehensive bifurcation study that incorporation of Allee effect enriches the local as well as the global dynamics of the system. Specially after a certain threshold value of the Allee effect, it has a very significant effect on the chaotic dynamics of the system. In course of the bifurcation analysis we have explored all possible bifurcations such as the existence of transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and Bautin bifurcation and period-doubling route to chaos respectively.https://www.aimspress.com/article/doi/10.3934/mbe.2018040prey-predatorallee effectstabilitybifurcationchaos |
| spellingShingle | Moitri Sen Malay Banerjee Yasuhiro Takeuchi Influence of Allee effect in prey populations on the dynamics of two-prey-one-predator model Mathematical Biosciences and Engineering prey-predator allee effect stability bifurcation chaos |
| title | Influence of Allee effect in prey populations on the dynamics of two-prey-one-predator model |
| title_full | Influence of Allee effect in prey populations on the dynamics of two-prey-one-predator model |
| title_fullStr | Influence of Allee effect in prey populations on the dynamics of two-prey-one-predator model |
| title_full_unstemmed | Influence of Allee effect in prey populations on the dynamics of two-prey-one-predator model |
| title_short | Influence of Allee effect in prey populations on the dynamics of two-prey-one-predator model |
| title_sort | influence of allee effect in prey populations on the dynamics of two prey one predator model |
| topic | prey-predator allee effect stability bifurcation chaos |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018040 |
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