Stability and Bifurcation Analysis of a Fractional-Order Food Chain Model with Two Time Delays
In this study, the stability and bifurcation problems of a fractional food chain system with two kinds of delays are studied. Firstly, the nonnegative, bounded, and unique properties of the solutions of the system are proved. The asymptotic stability of the equilibrium points of the system is discus...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/5313931 |
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| _version_ | 1850172255759237120 |
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| author | Hao Qi Wencai Zhao |
| author_facet | Hao Qi Wencai Zhao |
| author_sort | Hao Qi |
| collection | DOAJ |
| description | In this study, the stability and bifurcation problems of a fractional food chain system with two kinds of delays are studied. Firstly, the nonnegative, bounded, and unique properties of the solutions of the system are proved. The asymptotic stability of the equilibrium points of the system is discussed. Furthermore, the global asymptotic stability of the positive equilibrium point is deduced by using Lyapunov function method. Secondly, the system takes two kinds of time delays as bifurcation parameters and calculates the critical values of Hopf bifurcation accurately. The results show that Hopf bifurcation can advance with increasing fractional order and another delay. In conclusion, numerical simulation verifies and illustrates the theoretical results. |
| format | Article |
| id | doaj-art-cfa1594ff3d94424a220b080685bb4b9 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-cfa1594ff3d94424a220b080685bb4b92025-08-20T02:20:07ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/5313931Stability and Bifurcation Analysis of a Fractional-Order Food Chain Model with Two Time DelaysHao Qi0Wencai Zhao1College of Mathematics and Systems ScienceCollege of Mathematics and Systems ScienceIn this study, the stability and bifurcation problems of a fractional food chain system with two kinds of delays are studied. Firstly, the nonnegative, bounded, and unique properties of the solutions of the system are proved. The asymptotic stability of the equilibrium points of the system is discussed. Furthermore, the global asymptotic stability of the positive equilibrium point is deduced by using Lyapunov function method. Secondly, the system takes two kinds of time delays as bifurcation parameters and calculates the critical values of Hopf bifurcation accurately. The results show that Hopf bifurcation can advance with increasing fractional order and another delay. In conclusion, numerical simulation verifies and illustrates the theoretical results.http://dx.doi.org/10.1155/2022/5313931 |
| spellingShingle | Hao Qi Wencai Zhao Stability and Bifurcation Analysis of a Fractional-Order Food Chain Model with Two Time Delays Journal of Mathematics |
| title | Stability and Bifurcation Analysis of a Fractional-Order Food Chain Model with Two Time Delays |
| title_full | Stability and Bifurcation Analysis of a Fractional-Order Food Chain Model with Two Time Delays |
| title_fullStr | Stability and Bifurcation Analysis of a Fractional-Order Food Chain Model with Two Time Delays |
| title_full_unstemmed | Stability and Bifurcation Analysis of a Fractional-Order Food Chain Model with Two Time Delays |
| title_short | Stability and Bifurcation Analysis of a Fractional-Order Food Chain Model with Two Time Delays |
| title_sort | stability and bifurcation analysis of a fractional order food chain model with two time delays |
| url | http://dx.doi.org/10.1155/2022/5313931 |
| work_keys_str_mv | AT haoqi stabilityandbifurcationanalysisofafractionalorderfoodchainmodelwithtwotimedelays AT wencaizhao stabilityandbifurcationanalysisofafractionalorderfoodchainmodelwithtwotimedelays |