Controlling chaos in three species food chain model with fear effect
In this article, we study the impact of fear on the dynamics of a three species food chain model. We propose a model with the assumption that the growth rate of intermediate predator reduces at the cost of fear due to top predator, and the growth rate of prey is suppressed due to the fear of the int...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020056/fulltext.html |
| _version_ | 1818265570419671040 |
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| author | Vikas Kumar Nitu Kumari |
| author_facet | Vikas Kumar Nitu Kumari |
| author_sort | Vikas Kumar |
| collection | DOAJ |
| description | In this article, we study the impact of fear on the dynamics of a three species food chain model. We propose a model with the assumption that the growth rate of intermediate predator reduces at the cost of fear due to top predator, and the growth rate of prey is suppressed due to the fear of the intermediate predator. We carry out the existence of equilibria, local stability analysis and bifurcation analysis. Our numerical simulation reveals that for a low cost of the fear, system remains chaotic while increase in fear factor leads to stability. Even the large cost of fear causes the population to become extinct. We conclude that the fear effect can stabilize the chaotic dynamics of the system. |
| first_indexed | 2024-12-12T19:52:54Z |
| format | Article |
| id | doaj.art-c7d2a2ea95f04b99bb2c0dccba8ee5d5 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-12T19:52:54Z |
| publishDate | 2020-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-c7d2a2ea95f04b99bb2c0dccba8ee5d52022-12-22T00:13:56ZengAIMS PressAIMS Mathematics2473-69882020-01-015282884210.3934/math.2020056Controlling chaos in three species food chain model with fear effectVikas Kumar0Nitu Kumari1School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, 175005, IndiaSchool of Basic Sciences, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, 175005, IndiaIn this article, we study the impact of fear on the dynamics of a three species food chain model. We propose a model with the assumption that the growth rate of intermediate predator reduces at the cost of fear due to top predator, and the growth rate of prey is suppressed due to the fear of the intermediate predator. We carry out the existence of equilibria, local stability analysis and bifurcation analysis. Our numerical simulation reveals that for a low cost of the fear, system remains chaotic while increase in fear factor leads to stability. Even the large cost of fear causes the population to become extinct. We conclude that the fear effect can stabilize the chaotic dynamics of the system.https://www.aimspress.com/article/10.3934/math.2020056/fulltext.htmlfear effect. local stability. bifurcation. chaos. numerical simulation |
| spellingShingle | Vikas Kumar Nitu Kumari Controlling chaos in three species food chain model with fear effect AIMS Mathematics fear effect. local stability. bifurcation. chaos. numerical simulation |
| title | Controlling chaos in three species food chain model with fear effect |
| title_full | Controlling chaos in three species food chain model with fear effect |
| title_fullStr | Controlling chaos in three species food chain model with fear effect |
| title_full_unstemmed | Controlling chaos in three species food chain model with fear effect |
| title_short | Controlling chaos in three species food chain model with fear effect |
| title_sort | controlling chaos in three species food chain model with fear effect |
| topic | fear effect. local stability. bifurcation. chaos. numerical simulation |
| url | https://www.aimspress.com/article/10.3934/math.2020056/fulltext.html |
| work_keys_str_mv | AT vikaskumar controllingchaosinthreespeciesfoodchainmodelwithfeareffect AT nitukumari controllingchaosinthreespeciesfoodchainmodelwithfeareffect |