Dynamics Analysis and Optimal Control for a Delayed Rumor-Spreading Model
In this work, we analyze a delayed rumor-propagation model. First, we analyze the existence and boundedness of the solution of the model. Then, we give the conditions for the existence of the rumor-endemic equilibrium. Regrading the delay as a bifurcating parameter, we explore the local asymptotic s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/19/3455 |
| _version_ | 1797478220170264576 |
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| author | Chunru Li Zujun Ma |
| author_facet | Chunru Li Zujun Ma |
| author_sort | Chunru Li |
| collection | DOAJ |
| description | In this work, we analyze a delayed rumor-propagation model. First, we analyze the existence and boundedness of the solution of the model. Then, we give the conditions for the existence of the rumor-endemic equilibrium. Regrading the delay as a bifurcating parameter, we explore the local asymptotic stability and Hopf bifurcation of the rumor-endemic equilibrium. By a Lyapunov functional technique, we examine the global asymptotically stability of the rumor-free and the rumor-endemic equilibria. We provide two control variables in the rumor-spreading model with time delay, and get the optimal solution via the optimal procedures. Finally, we present some numerical simulations to verify our theoretical predictions. They illustrate that the delay is a crucial issue for system, and it can lead to not just Hopf bifurcation but also chaos. |
| first_indexed | 2024-03-09T21:28:55Z |
| format | Article |
| id | doaj.art-cb059762991a48cb946ed0369f2fb5f6 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T21:28:55Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-cb059762991a48cb946ed0369f2fb5f62023-11-23T21:01:48ZengMDPI AGMathematics2227-73902022-09-011019345510.3390/math10193455Dynamics Analysis and Optimal Control for a Delayed Rumor-Spreading ModelChunru Li0Zujun Ma1Business School, Changshu Institute of Technology, Changshu 215500, ChinaSchool of Economics and Management, Southwest Jiaotong University, Chengdu 610031, ChinaIn this work, we analyze a delayed rumor-propagation model. First, we analyze the existence and boundedness of the solution of the model. Then, we give the conditions for the existence of the rumor-endemic equilibrium. Regrading the delay as a bifurcating parameter, we explore the local asymptotic stability and Hopf bifurcation of the rumor-endemic equilibrium. By a Lyapunov functional technique, we examine the global asymptotically stability of the rumor-free and the rumor-endemic equilibria. We provide two control variables in the rumor-spreading model with time delay, and get the optimal solution via the optimal procedures. Finally, we present some numerical simulations to verify our theoretical predictions. They illustrate that the delay is a crucial issue for system, and it can lead to not just Hopf bifurcation but also chaos.https://www.mdpi.com/2227-7390/10/19/3455rumor spreading modeldelaybifurcationglobal stabilitychaos |
| spellingShingle | Chunru Li Zujun Ma Dynamics Analysis and Optimal Control for a Delayed Rumor-Spreading Model Mathematics rumor spreading model delay bifurcation global stability chaos |
| title | Dynamics Analysis and Optimal Control for a Delayed Rumor-Spreading Model |
| title_full | Dynamics Analysis and Optimal Control for a Delayed Rumor-Spreading Model |
| title_fullStr | Dynamics Analysis and Optimal Control for a Delayed Rumor-Spreading Model |
| title_full_unstemmed | Dynamics Analysis and Optimal Control for a Delayed Rumor-Spreading Model |
| title_short | Dynamics Analysis and Optimal Control for a Delayed Rumor-Spreading Model |
| title_sort | dynamics analysis and optimal control for a delayed rumor spreading model |
| topic | rumor spreading model delay bifurcation global stability chaos |
| url | https://www.mdpi.com/2227-7390/10/19/3455 |
| work_keys_str_mv | AT chunruli dynamicsanalysisandoptimalcontrolforadelayedrumorspreadingmodel AT zujunma dynamicsanalysisandoptimalcontrolforadelayedrumorspreadingmodel |