Dynamical study of the theta-logistic predator-prey model incorporating gregarious behavior of prey
Relation between species and their livelihood environment in ecological systems is very complex. For that reason, in order to study predator-prey relations, modeling is essential in biomathematics. The vital components of predator-prey models are prey species' growth function in the absence of...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Western Libraries
2023-05-01
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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/15648 |
| _version_ | 1827856711447216128 |
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| author | P. K. Santra G. S. Mahapatra |
| author_facet | P. K. Santra G. S. Mahapatra |
| author_sort | P. K. Santra |
| collection | DOAJ |
| description | Relation between species and their livelihood environment in ecological systems is very complex. For that reason, in order to study predator-prey relations, modeling is essential in biomathematics. The vital components of predator-prey models are prey species' growth function in the absence of a
predator and the functional response. In this article, we proposed a predator-prey model with gregarious prey. In the existing literature, square-root functional response incorporates the gregarious behavior of prey. This study considers the generalized square root functional response and theta-logistic growth of prey in the absence of a predator. The effect of functional response parameters on stability, limit cycle, and Hopf bifurcation on the proposed model has been discussed. Numerical analysis is performed on the basis of some hypothetical parameter values to analyze the model numerically. |
| first_indexed | 2024-03-12T12:29:44Z |
| format | Article |
| id | doaj.art-7f29fb60a4534fb4a0941f458a738fa4 |
| institution | Directory Open Access Journal |
| issn | 2563-1926 |
| language | English |
| last_indexed | 2024-03-12T12:29:44Z |
| publishDate | 2023-05-01 |
| publisher | Western Libraries |
| record_format | Article |
| series | Mathematics in Applied Sciences and Engineering |
| spelling | doaj.art-7f29fb60a4534fb4a0941f458a738fa42023-08-29T14:29:48ZengWestern LibrariesMathematics in Applied Sciences and Engineering2563-19262023-05-014210011410.5206/mase/156489892Dynamical study of the theta-logistic predator-prey model incorporating gregarious behavior of preyP. K. Santra0G. S. Mahapatra1Abada Nsup SchoolDepartment of Mathematics, National Institute of Technology Puducherry, Karaikal-609609, India.Relation between species and their livelihood environment in ecological systems is very complex. For that reason, in order to study predator-prey relations, modeling is essential in biomathematics. The vital components of predator-prey models are prey species' growth function in the absence of a predator and the functional response. In this article, we proposed a predator-prey model with gregarious prey. In the existing literature, square-root functional response incorporates the gregarious behavior of prey. This study considers the generalized square root functional response and theta-logistic growth of prey in the absence of a predator. The effect of functional response parameters on stability, limit cycle, and Hopf bifurcation on the proposed model has been discussed. Numerical analysis is performed on the basis of some hypothetical parameter values to analyze the model numerically.https://ojs.lib.uwo.ca/index.php/mase/article/view/15648predator-preyfunctional responselimit cyclestabilityhopf bifurcation. |
| spellingShingle | P. K. Santra G. S. Mahapatra Dynamical study of the theta-logistic predator-prey model incorporating gregarious behavior of prey Mathematics in Applied Sciences and Engineering predator-prey functional response limit cycle stability hopf bifurcation. |
| title | Dynamical study of the theta-logistic predator-prey model incorporating gregarious behavior of prey |
| title_full | Dynamical study of the theta-logistic predator-prey model incorporating gregarious behavior of prey |
| title_fullStr | Dynamical study of the theta-logistic predator-prey model incorporating gregarious behavior of prey |
| title_full_unstemmed | Dynamical study of the theta-logistic predator-prey model incorporating gregarious behavior of prey |
| title_short | Dynamical study of the theta-logistic predator-prey model incorporating gregarious behavior of prey |
| title_sort | dynamical study of the theta logistic predator prey model incorporating gregarious behavior of prey |
| topic | predator-prey functional response limit cycle stability hopf bifurcation. |
| url | https://ojs.lib.uwo.ca/index.php/mase/article/view/15648 |
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