Hopf bifurcation exploration and control technique in a predator-prey system incorporating delay
Recently, delayed dynamical model has witnessed a great interest from many scholars in biological and mathematical areas due to its potential application in describing the interaction of different biological populations. In this article, relying the previous studies, we set up two new predator-prey...
| Main Authors: | , , , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-01-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024080?viewType=HTML |
| _version_ | 1797357931865309184 |
|---|---|
| author | Wei Ou Changjin Xu Qingyi Cui Yicheng Pang Zixin Liu Jianwei Shen Muhammad Zafarullah Baber Muhammad Farman Shabir Ahmad |
| author_facet | Wei Ou Changjin Xu Qingyi Cui Yicheng Pang Zixin Liu Jianwei Shen Muhammad Zafarullah Baber Muhammad Farman Shabir Ahmad |
| author_sort | Wei Ou |
| collection | DOAJ |
| description | Recently, delayed dynamical model has witnessed a great interest from many scholars in biological and mathematical areas due to its potential application in describing the interaction of different biological populations. In this article, relying the previous studies, we set up two new predator-prey systems incorporating delay. By virtue of fixed point theory, inequality tactics and an appropriate function, we explore well-posedness (includes existence and uniqueness, boundedness and non-negativeness) of the solution of the two formulated delayed predator-prey systems. With the aid of bifurcation theorem and stability theory of delayed differential equations, we gain the parameter conditions on the emergence of stability and bifurcation phenomenon of the two formulated delayed predator-prey systems. By applying two controllers (hybrid controller and extended delayed feedback controller) we can efficaciously regulate the region of stability and the time of occurrence of bifurcation phenomenon for the two delayed predator-prey systems. The effect of delay on stabilizing the system and adjusting bifurcation is investigated. Computer simulation plots are provided to sustain the acquired prime outcomes. The conclusions of this article are completely new and can provide some momentous instructions in dominating and balancing the densities of predator and prey. |
| first_indexed | 2024-03-08T14:52:37Z |
| format | Article |
| id | doaj.art-9334ddd89af546be9b234a3df08a275d |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T14:52:37Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-9334ddd89af546be9b234a3df08a275d2024-01-11T01:30:57ZengAIMS PressAIMS Mathematics2473-69882024-01-01911622165110.3934/math.2024080Hopf bifurcation exploration and control technique in a predator-prey system incorporating delayWei Ou0Changjin Xu1Qingyi Cui2 Yicheng Pang3Zixin Liu 4Jianwei Shen5Muhammad Zafarullah Baber6Muhammad Farman 7Shabir Ahmad81. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China2. Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550025, China1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China3. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China4. Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan5. Department of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Rahim Yar Khan 64200, Pakistan 6. Faculty of Aets and Science, Department of Mathematics, Near East University, Cyprus 7. Department of Computer Science and Mathematics, Lebanese American University, 1107-2020, Beirut, Lebanon8. Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, PakistanRecently, delayed dynamical model has witnessed a great interest from many scholars in biological and mathematical areas due to its potential application in describing the interaction of different biological populations. In this article, relying the previous studies, we set up two new predator-prey systems incorporating delay. By virtue of fixed point theory, inequality tactics and an appropriate function, we explore well-posedness (includes existence and uniqueness, boundedness and non-negativeness) of the solution of the two formulated delayed predator-prey systems. With the aid of bifurcation theorem and stability theory of delayed differential equations, we gain the parameter conditions on the emergence of stability and bifurcation phenomenon of the two formulated delayed predator-prey systems. By applying two controllers (hybrid controller and extended delayed feedback controller) we can efficaciously regulate the region of stability and the time of occurrence of bifurcation phenomenon for the two delayed predator-prey systems. The effect of delay on stabilizing the system and adjusting bifurcation is investigated. Computer simulation plots are provided to sustain the acquired prime outcomes. The conclusions of this article are completely new and can provide some momentous instructions in dominating and balancing the densities of predator and prey.https://www.aimspress.com/article/doi/10.3934/math.2024080?viewType=HTMLpredator-prey systemwell-posednesshopf bifurcationstabilityhybrid controllerdelay |
| spellingShingle | Wei Ou Changjin Xu Qingyi Cui Yicheng Pang Zixin Liu Jianwei Shen Muhammad Zafarullah Baber Muhammad Farman Shabir Ahmad Hopf bifurcation exploration and control technique in a predator-prey system incorporating delay AIMS Mathematics predator-prey system well-posedness hopf bifurcation stability hybrid controller delay |
| title | Hopf bifurcation exploration and control technique in a predator-prey system incorporating delay |
| title_full | Hopf bifurcation exploration and control technique in a predator-prey system incorporating delay |
| title_fullStr | Hopf bifurcation exploration and control technique in a predator-prey system incorporating delay |
| title_full_unstemmed | Hopf bifurcation exploration and control technique in a predator-prey system incorporating delay |
| title_short | Hopf bifurcation exploration and control technique in a predator-prey system incorporating delay |
| title_sort | hopf bifurcation exploration and control technique in a predator prey system incorporating delay |
| topic | predator-prey system well-posedness hopf bifurcation stability hybrid controller delay |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024080?viewType=HTML |
| work_keys_str_mv | AT weiou hopfbifurcationexplorationandcontroltechniqueinapredatorpreysystemincorporatingdelay AT changjinxu hopfbifurcationexplorationandcontroltechniqueinapredatorpreysystemincorporatingdelay AT qingyicui hopfbifurcationexplorationandcontroltechniqueinapredatorpreysystemincorporatingdelay AT yichengpang hopfbifurcationexplorationandcontroltechniqueinapredatorpreysystemincorporatingdelay AT zixinliu hopfbifurcationexplorationandcontroltechniqueinapredatorpreysystemincorporatingdelay AT jianweishen hopfbifurcationexplorationandcontroltechniqueinapredatorpreysystemincorporatingdelay AT muhammadzafarullahbaber hopfbifurcationexplorationandcontroltechniqueinapredatorpreysystemincorporatingdelay AT muhammadfarman hopfbifurcationexplorationandcontroltechniqueinapredatorpreysystemincorporatingdelay AT shabirahmad hopfbifurcationexplorationandcontroltechniqueinapredatorpreysystemincorporatingdelay |