Stability Switching Curves and Hopf Bifurcation of a Fractional Predator–Prey System with Two Nonidentical Delays
In this paper, we propose and analyze a three-dimensional fractional predator–prey system with two nonidentical delays. By choosing two delays as the bifurcation parameter, we first calculate the stability switching curves in the delay plane. By judging the direction of the characteristic root acros...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/4/643 |
| _version_ | 1797409265505271808 |
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| author | Shuangfei Li Yingxian Zhu Yunxian Dai Yiping Lin |
| author_facet | Shuangfei Li Yingxian Zhu Yunxian Dai Yiping Lin |
| author_sort | Shuangfei Li |
| collection | DOAJ |
| description | In this paper, we propose and analyze a three-dimensional fractional predator–prey system with two nonidentical delays. By choosing two delays as the bifurcation parameter, we first calculate the stability switching curves in the delay plane. By judging the direction of the characteristic root across the imaginary axis in stability switching curves, we obtain that the stability of the system changes when two delays cross the stability switching curves, and then, the system appears to have bifurcating periodic solutions near the positive equilibrium, which implies that the trajectory of the system is the axial symmetry. Secondly, we obtain the conditions for the existence of Hopf bifurcation. Finally, we give one example to verify the correctness of the theoretical analysis. In particular, the geometric stability switch criteria are applied to the stability analysis of the fractional differential predator–prey system with two delays for the first time. |
| first_indexed | 2024-03-09T04:11:49Z |
| format | Article |
| id | doaj.art-95935ab658024cefa0aa863a0aea787b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T04:11:49Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-95935ab658024cefa0aa863a0aea787b2023-12-03T13:59:50ZengMDPI AGSymmetry2073-89942022-03-0114464310.3390/sym14040643Stability Switching Curves and Hopf Bifurcation of a Fractional Predator–Prey System with Two Nonidentical DelaysShuangfei Li0Yingxian Zhu1Yunxian Dai2Yiping Lin3Department of System Science and Applied Mathematics, Kunming University of Science and Technology, Kunming 650500, ChinaDepartment of System Science and Applied Mathematics, Kunming University of Science and Technology, Kunming 650500, ChinaDepartment of System Science and Applied Mathematics, Kunming University of Science and Technology, Kunming 650500, ChinaDepartment of System Science and Applied Mathematics, Kunming University of Science and Technology, Kunming 650500, ChinaIn this paper, we propose and analyze a three-dimensional fractional predator–prey system with two nonidentical delays. By choosing two delays as the bifurcation parameter, we first calculate the stability switching curves in the delay plane. By judging the direction of the characteristic root across the imaginary axis in stability switching curves, we obtain that the stability of the system changes when two delays cross the stability switching curves, and then, the system appears to have bifurcating periodic solutions near the positive equilibrium, which implies that the trajectory of the system is the axial symmetry. Secondly, we obtain the conditions for the existence of Hopf bifurcation. Finally, we give one example to verify the correctness of the theoretical analysis. In particular, the geometric stability switch criteria are applied to the stability analysis of the fractional differential predator–prey system with two delays for the first time.https://www.mdpi.com/2073-8994/14/4/643fractional ordertwo delaysstability switching curvesaxial symmetryHopf bifurcation |
| spellingShingle | Shuangfei Li Yingxian Zhu Yunxian Dai Yiping Lin Stability Switching Curves and Hopf Bifurcation of a Fractional Predator–Prey System with Two Nonidentical Delays Symmetry fractional order two delays stability switching curves axial symmetry Hopf bifurcation |
| title | Stability Switching Curves and Hopf Bifurcation of a Fractional Predator–Prey System with Two Nonidentical Delays |
| title_full | Stability Switching Curves and Hopf Bifurcation of a Fractional Predator–Prey System with Two Nonidentical Delays |
| title_fullStr | Stability Switching Curves and Hopf Bifurcation of a Fractional Predator–Prey System with Two Nonidentical Delays |
| title_full_unstemmed | Stability Switching Curves and Hopf Bifurcation of a Fractional Predator–Prey System with Two Nonidentical Delays |
| title_short | Stability Switching Curves and Hopf Bifurcation of a Fractional Predator–Prey System with Two Nonidentical Delays |
| title_sort | stability switching curves and hopf bifurcation of a fractional predator prey system with two nonidentical delays |
| topic | fractional order two delays stability switching curves axial symmetry Hopf bifurcation |
| url | https://www.mdpi.com/2073-8994/14/4/643 |
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