Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks
In recent years, with the rapid development of the Internet and the Internet of Things, network security is urgently needed. Malware becomes a major threat to network security. Thus, the study on malware propagation model plays an important role in network security. In the past few decades, numerous...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2019/7057052 |
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| _version_ | 1832561313151188992 |
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| author | Changjin Xu Maoxin Liao Peiluan Li |
| author_facet | Changjin Xu Maoxin Liao Peiluan Li |
| author_sort | Changjin Xu |
| collection | DOAJ |
| description | In recent years, with the rapid development of the Internet and the Internet of Things, network security is urgently needed. Malware becomes a major threat to network security. Thus, the study on malware propagation model plays an important role in network security. In the past few decades, numerous researchers put up various kinds of malware propagation models to analyze the dynamic interaction. However, many works are only concerned with the integer-order malware propagation models, while the investigation on fractional-order ones is very few. In this paper, based on the earlier works, we will put up a new fractional-order delayed malware propagation model. Letting the delay be bifurcation parameter and analyzing the corresponding characteristic equations of considered system, we will establish a set of new sufficient conditions to guarantee the stability and the existence of Hopf bifurcation of fractional-order delayed malware propagation model. The study shows that the delay and the fractional order have important effect on the stability and Hopf bifurcation of considered system. To check the correctness of theoretical analyses, we carry out some computer simulations. At last, a simple conclusion is drawn. The derived results of this paper are completely innovative and play an important guiding role in network security. |
| format | Article |
| id | doaj-art-b965ccb865c54da7a6852610fc7c0091 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-b965ccb865c54da7a6852610fc7c00912025-02-03T01:25:22ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/70570527057052Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social NetworksChangjin Xu0Maoxin Liao1Peiluan Li2Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, ChinaSchool of Mathematics and Physics, University of South China, Hengyang 421001, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaIn recent years, with the rapid development of the Internet and the Internet of Things, network security is urgently needed. Malware becomes a major threat to network security. Thus, the study on malware propagation model plays an important role in network security. In the past few decades, numerous researchers put up various kinds of malware propagation models to analyze the dynamic interaction. However, many works are only concerned with the integer-order malware propagation models, while the investigation on fractional-order ones is very few. In this paper, based on the earlier works, we will put up a new fractional-order delayed malware propagation model. Letting the delay be bifurcation parameter and analyzing the corresponding characteristic equations of considered system, we will establish a set of new sufficient conditions to guarantee the stability and the existence of Hopf bifurcation of fractional-order delayed malware propagation model. The study shows that the delay and the fractional order have important effect on the stability and Hopf bifurcation of considered system. To check the correctness of theoretical analyses, we carry out some computer simulations. At last, a simple conclusion is drawn. The derived results of this paper are completely innovative and play an important guiding role in network security.http://dx.doi.org/10.1155/2019/7057052 |
| spellingShingle | Changjin Xu Maoxin Liao Peiluan Li Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks Discrete Dynamics in Nature and Society |
| title | Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks |
| title_full | Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks |
| title_fullStr | Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks |
| title_full_unstemmed | Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks |
| title_short | Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks |
| title_sort | bifurcation of a fractional order delayed malware propagation model in social networks |
| url | http://dx.doi.org/10.1155/2019/7057052 |
| work_keys_str_mv | AT changjinxu bifurcationofafractionalorderdelayedmalwarepropagationmodelinsocialnetworks AT maoxinliao bifurcationofafractionalorderdelayedmalwarepropagationmodelinsocialnetworks AT peiluanli bifurcationofafractionalorderdelayedmalwarepropagationmodelinsocialnetworks |