Stability Analysis of a Fractional-Order SEIR-KS Computer Virus-Spreading Model with Two Delays
In this paper, the stability and Hopf bifurcation of a fractional-order model of the Susceptible-Exposed-Infected-Kill Signals Recovered (SEIR-KS) computer virus with two delays are studied. The sufficient conditions for solving the stability and the occurrence of Hopf bifurcation of the system are...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6144953 |
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| _version_ | 1832566435121987584 |
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| author | Zhufeng Wang Xiaoqian Nie Maoxin Liao |
| author_facet | Zhufeng Wang Xiaoqian Nie Maoxin Liao |
| author_sort | Zhufeng Wang |
| collection | DOAJ |
| description | In this paper, the stability and Hopf bifurcation of a fractional-order model of the Susceptible-Exposed-Infected-Kill Signals Recovered (SEIR-KS) computer virus with two delays are studied. The sufficient conditions for solving the stability and the occurrence of Hopf bifurcation of the system are established by using Laplace transform, stability theory, and Hopf bifurcation theorem of fractional-order differential systems. The research shows that time delays and fractional order q have an important effect on the stability and the emergence of Hopf bifurcation of the fractional computer virus model. In addition, the validity of the theoretical analysis is verified by selecting appropriate system parameters for numerical simulation and the biological correlation of the equilibrium point is discussed. The results show that the bifurcation point of the model increases with the decrease in the model fractional order q. Under the same fractional order q, the effects of different types of delays on bifurcation points are obviously different. |
| format | Article |
| id | doaj-art-bcb93bbd1993443394bd7d9ceddee6ca |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-bcb93bbd1993443394bd7d9ceddee6ca2025-02-03T01:04:17ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/61449536144953Stability Analysis of a Fractional-Order SEIR-KS Computer Virus-Spreading Model with Two DelaysZhufeng Wang0Xiaoqian Nie1Maoxin Liao2Department of Foundation, Southwest Jiaotong University Hope College, Chengdu, Sichuan 610400, ChinaDepartment of Accounting, Southwest Jiaotong University Hope College, Chengdu, Sichuan 610400, ChinaSchool of Mathematics and Physics, University of South China, Hengyang, Hunan 421001, ChinaIn this paper, the stability and Hopf bifurcation of a fractional-order model of the Susceptible-Exposed-Infected-Kill Signals Recovered (SEIR-KS) computer virus with two delays are studied. The sufficient conditions for solving the stability and the occurrence of Hopf bifurcation of the system are established by using Laplace transform, stability theory, and Hopf bifurcation theorem of fractional-order differential systems. The research shows that time delays and fractional order q have an important effect on the stability and the emergence of Hopf bifurcation of the fractional computer virus model. In addition, the validity of the theoretical analysis is verified by selecting appropriate system parameters for numerical simulation and the biological correlation of the equilibrium point is discussed. The results show that the bifurcation point of the model increases with the decrease in the model fractional order q. Under the same fractional order q, the effects of different types of delays on bifurcation points are obviously different.http://dx.doi.org/10.1155/2021/6144953 |
| spellingShingle | Zhufeng Wang Xiaoqian Nie Maoxin Liao Stability Analysis of a Fractional-Order SEIR-KS Computer Virus-Spreading Model with Two Delays Journal of Mathematics |
| title | Stability Analysis of a Fractional-Order SEIR-KS Computer Virus-Spreading Model with Two Delays |
| title_full | Stability Analysis of a Fractional-Order SEIR-KS Computer Virus-Spreading Model with Two Delays |
| title_fullStr | Stability Analysis of a Fractional-Order SEIR-KS Computer Virus-Spreading Model with Two Delays |
| title_full_unstemmed | Stability Analysis of a Fractional-Order SEIR-KS Computer Virus-Spreading Model with Two Delays |
| title_short | Stability Analysis of a Fractional-Order SEIR-KS Computer Virus-Spreading Model with Two Delays |
| title_sort | stability analysis of a fractional order seir ks computer virus spreading model with two delays |
| url | http://dx.doi.org/10.1155/2021/6144953 |
| work_keys_str_mv | AT zhufengwang stabilityanalysisofafractionalorderseirkscomputervirusspreadingmodelwithtwodelays AT xiaoqiannie stabilityanalysisofafractionalorderseirkscomputervirusspreadingmodelwithtwodelays AT maoxinliao stabilityanalysisofafractionalorderseirkscomputervirusspreadingmodelwithtwodelays |