Study on a fractional order delayed predator-prey model including prey refuge and type II functional response
The fractional-order delayed predator-prey dynamical scheme studied here includes a prey refuge with Holling type-II functional response. The existence and uniqueness of a solution for our scheme are explored. Hopf bifurcation with respect to delay is reconnoitered, besides local and global stabilit...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818123000682 |
| _version_ | 1797390352064184320 |
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| author | K. Ramesh G. Ranjith Kumar Kottakkaran Sooppy Nisar K. Lakshminarayan K. Kondala Rao Wedad Albalawi Abdel-Haleem Abdel-Aty |
| author_facet | K. Ramesh G. Ranjith Kumar Kottakkaran Sooppy Nisar K. Lakshminarayan K. Kondala Rao Wedad Albalawi Abdel-Haleem Abdel-Aty |
| author_sort | K. Ramesh |
| collection | DOAJ |
| description | The fractional-order delayed predator-prey dynamical scheme studied here includes a prey refuge with Holling type-II functional response. The existence and uniqueness of a solution for our scheme are explored. Hopf bifurcation with respect to delay is reconnoitered, besides local and global stability of existing steady states of fractional order0 < q ≤ 1. It is discovered that the delay passes through a series of crucial values when Hopf bifurcation takes place. Additionally, both theoretically and statistically, the impacts of prey refuge effects and fractional order on system stability are investigated. The delayed differential scheme's dynamics and results durability are improved by fractional order. Fractional order enhances the stability of the solutions and enriches the dynamics of the delayed differential model. Additionally, both theoretically and by the use of numerical simulations, the effects of fractional order and the prey refuge effects on the stability of the system are investigated. |
| first_indexed | 2024-03-08T23:10:28Z |
| format | Article |
| id | doaj.art-7e59af97f8fe41af8580cf83b7ea90a1 |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-03-08T23:10:28Z |
| publishDate | 2023-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-7e59af97f8fe41af8580cf83b7ea90a12023-12-15T07:26:46ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812023-12-018100555Study on a fractional order delayed predator-prey model including prey refuge and type II functional responseK. Ramesh0G. Ranjith Kumar1Kottakkaran Sooppy Nisar2K. Lakshminarayan3K. Kondala Rao4Wedad Albalawi5Abdel-Haleem Abdel-Aty6Department of Mathematics, Anurag University, Venkatapur, Hyderabad, Telangana 500088, IndiaDepartment of Mathematics, Anurag University, Venkatapur, Hyderabad, Telangana 500088, IndiaDepartment of Mathematics, College of science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Saudi Arabia; Corresponding author.Department of Mathematics, Vidya Jyothi Institute of Technology, Hyderabad, Telangana 500075, IndiaDepartment of Mathematics, Vidya Jyothi Institute of Technology, Hyderabad, Telangana 500075, IndiaDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Physics, College of Sciences, University of Bisha, PO Box 344, Bisha 61922, Saudi ArabiaThe fractional-order delayed predator-prey dynamical scheme studied here includes a prey refuge with Holling type-II functional response. The existence and uniqueness of a solution for our scheme are explored. Hopf bifurcation with respect to delay is reconnoitered, besides local and global stability of existing steady states of fractional order0 < q ≤ 1. It is discovered that the delay passes through a series of crucial values when Hopf bifurcation takes place. Additionally, both theoretically and statistically, the impacts of prey refuge effects and fractional order on system stability are investigated. The delayed differential scheme's dynamics and results durability are improved by fractional order. Fractional order enhances the stability of the solutions and enriches the dynamics of the delayed differential model. Additionally, both theoretically and by the use of numerical simulations, the effects of fractional order and the prey refuge effects on the stability of the system are investigated.http://www.sciencedirect.com/science/article/pii/S2666818123000682Predator-prey modelCaputo fractional derivativePrey refugeTime-delayStabilityNumerical simulations |
| spellingShingle | K. Ramesh G. Ranjith Kumar Kottakkaran Sooppy Nisar K. Lakshminarayan K. Kondala Rao Wedad Albalawi Abdel-Haleem Abdel-Aty Study on a fractional order delayed predator-prey model including prey refuge and type II functional response Partial Differential Equations in Applied Mathematics Predator-prey model Caputo fractional derivative Prey refuge Time-delay Stability Numerical simulations |
| title | Study on a fractional order delayed predator-prey model including prey refuge and type II functional response |
| title_full | Study on a fractional order delayed predator-prey model including prey refuge and type II functional response |
| title_fullStr | Study on a fractional order delayed predator-prey model including prey refuge and type II functional response |
| title_full_unstemmed | Study on a fractional order delayed predator-prey model including prey refuge and type II functional response |
| title_short | Study on a fractional order delayed predator-prey model including prey refuge and type II functional response |
| title_sort | study on a fractional order delayed predator prey model including prey refuge and type ii functional response |
| topic | Predator-prey model Caputo fractional derivative Prey refuge Time-delay Stability Numerical simulations |
| url | http://www.sciencedirect.com/science/article/pii/S2666818123000682 |
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