Dynamics of a controlled discrete prey-predator model with Holling type-II functional response
This article investigates the complex dynamic behavior of a discrete predator-prey model with Holling type II functional response. Firstly, we discuss the local stability of the system at the equilibrium points. Secondly, we use the central manifold theorem and bifurcation theory to prove that two...
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| Format: | Article |
| Language: | English |
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Western Libraries
2024-09-01
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| Series: | Mathematics in Applied Sciences and Engineering |
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| Online Access: | https://ojs.lib.uwo.ca/index.php/mase/article/view/18643 |
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| _version_ | 1841560692018118656 |
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| author | Yanlin Min Xiaoling Han Ceyu Lei |
| author_facet | Yanlin Min Xiaoling Han Ceyu Lei |
| author_sort | Yanlin Min |
| collection | DOAJ |
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This article investigates the complex dynamic behavior of a discrete predator-prey model with Holling type II functional response. Firstly, we discuss the local stability of the system at the equilibrium points. Secondly, we use the central manifold theorem and bifurcation theory to prove that two different types of bifurcations in the system, namely flip bifurcation and Hopf bifurcation. Through numerical simulation, we validate the impact of human control parameters of predators and the degree of predator utilization on system dynamics. The results indicate that studying the predator-prey relationship between species in plateau pastoral areas can help humans better predict the population changes of prey and predator, and have great significance for the protection of ecosystems.
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| format | Article |
| id | doaj-art-3c1eb364e9fc413e9cf56c3649c768b0 |
| institution | Kabale University |
| issn | 2563-1926 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Western Libraries |
| record_format | Article |
| series | Mathematics in Applied Sciences and Engineering |
| spelling | doaj-art-3c1eb364e9fc413e9cf56c3649c768b02025-01-03T18:35:35ZengWestern LibrariesMathematics in Applied Sciences and Engineering2563-19262024-09-015410.5206/mase/18643Dynamics of a controlled discrete prey-predator model with Holling type-II functional responseYanlin MinXiaoling HanCeyu Lei This article investigates the complex dynamic behavior of a discrete predator-prey model with Holling type II functional response. Firstly, we discuss the local stability of the system at the equilibrium points. Secondly, we use the central manifold theorem and bifurcation theory to prove that two different types of bifurcations in the system, namely flip bifurcation and Hopf bifurcation. Through numerical simulation, we validate the impact of human control parameters of predators and the degree of predator utilization on system dynamics. The results indicate that studying the predator-prey relationship between species in plateau pastoral areas can help humans better predict the population changes of prey and predator, and have great significance for the protection of ecosystems. https://ojs.lib.uwo.ca/index.php/mase/article/view/18643Discrete model; flip bifurcation; Hopf bifurcation; bifurcation theory; chaos. |
| spellingShingle | Yanlin Min Xiaoling Han Ceyu Lei Dynamics of a controlled discrete prey-predator model with Holling type-II functional response Mathematics in Applied Sciences and Engineering Discrete model; flip bifurcation; Hopf bifurcation; bifurcation theory; chaos. |
| title | Dynamics of a controlled discrete prey-predator model with Holling type-II functional response |
| title_full | Dynamics of a controlled discrete prey-predator model with Holling type-II functional response |
| title_fullStr | Dynamics of a controlled discrete prey-predator model with Holling type-II functional response |
| title_full_unstemmed | Dynamics of a controlled discrete prey-predator model with Holling type-II functional response |
| title_short | Dynamics of a controlled discrete prey-predator model with Holling type-II functional response |
| title_sort | dynamics of a controlled discrete prey predator model with holling type ii functional response |
| topic | Discrete model; flip bifurcation; Hopf bifurcation; bifurcation theory; chaos. |
| url | https://ojs.lib.uwo.ca/index.php/mase/article/view/18643 |
| work_keys_str_mv | AT yanlinmin dynamicsofacontrolleddiscretepreypredatormodelwithhollingtypeiifunctionalresponse AT xiaolinghan dynamicsofacontrolleddiscretepreypredatormodelwithhollingtypeiifunctionalresponse AT ceyulei dynamicsofacontrolleddiscretepreypredatormodelwithhollingtypeiifunctionalresponse |