Analysis and Control of Malware Mutation Model in Wireless Rechargeable Sensor Network with Charging Delay
In wireless rechargeable sensors (WRSNs), the system is vulnerable to be attacked by malware. Because of the distributed network structure of WRSNs, the malware attack has great influence on the security system of WRSNs. With the variability in malware, the problem of decryption and coding errors wi...
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| Format: | Article |
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/14/2376 |
| _version_ | 1797433332164722688 |
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| author | Guiyun Liu Zhimin Peng Zhongwei Liang Xiaojing Zhong Xinhai Xia |
| author_facet | Guiyun Liu Zhimin Peng Zhongwei Liang Xiaojing Zhong Xinhai Xia |
| author_sort | Guiyun Liu |
| collection | DOAJ |
| description | In wireless rechargeable sensors (WRSNs), the system is vulnerable to be attacked by malware. Because of the distributed network structure of WRSNs, the malware attack has great influence on the security system of WRSNs. With the variability in malware, the problem of decryption and coding errors will lead to the malware mutating. In this paper, there are two problems to be solved, including the malware mutation and the charging delay in WRSNs. The malware mutation state and the low-energy state are introduced. Firstly, three different equilibrium solutions of the mutation model are given. Then, the local stability is proven by the characteristic equation, and the system will be stabilized at different equilibrium solutions when the base reproductive number is different. With the condition of charging delay, the bifurcation phenomenon is investigated by using the Hopf bifurcation theory. Furthermore, to improve the security of WRSNs and decrease the control cost, the Pontryagin’s Maximum principle is applied to obtain an optimal control scheme under mutation and charging delay. Finally, the numerical simulation is applied by Matlab to confirm this model. The simulation results show that the mutation malware can be controlled when the delay is less than the maximum threshold. |
| first_indexed | 2024-03-09T10:15:32Z |
| format | Article |
| id | doaj.art-8b0a67c63dc04ef99d43efb12251d369 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T10:15:32Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-8b0a67c63dc04ef99d43efb12251d3692023-12-01T22:24:24ZengMDPI AGMathematics2227-73902022-07-011014237610.3390/math10142376Analysis and Control of Malware Mutation Model in Wireless Rechargeable Sensor Network with Charging DelayGuiyun Liu0Zhimin Peng1Zhongwei Liang2Xiaojing Zhong3Xinhai Xia4School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, ChinaSchool of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, ChinaSchool of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, ChinaSchool of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, ChinaDepartment of Port and Shipping Management, Guangzhou Maritime University, Guangzhou 510725, ChinaIn wireless rechargeable sensors (WRSNs), the system is vulnerable to be attacked by malware. Because of the distributed network structure of WRSNs, the malware attack has great influence on the security system of WRSNs. With the variability in malware, the problem of decryption and coding errors will lead to the malware mutating. In this paper, there are two problems to be solved, including the malware mutation and the charging delay in WRSNs. The malware mutation state and the low-energy state are introduced. Firstly, three different equilibrium solutions of the mutation model are given. Then, the local stability is proven by the characteristic equation, and the system will be stabilized at different equilibrium solutions when the base reproductive number is different. With the condition of charging delay, the bifurcation phenomenon is investigated by using the Hopf bifurcation theory. Furthermore, to improve the security of WRSNs and decrease the control cost, the Pontryagin’s Maximum principle is applied to obtain an optimal control scheme under mutation and charging delay. Finally, the numerical simulation is applied by Matlab to confirm this model. The simulation results show that the mutation malware can be controlled when the delay is less than the maximum threshold.https://www.mdpi.com/2227-7390/10/14/2376WRSNsstable analysisHopf bifurcationoptimal control |
| spellingShingle | Guiyun Liu Zhimin Peng Zhongwei Liang Xiaojing Zhong Xinhai Xia Analysis and Control of Malware Mutation Model in Wireless Rechargeable Sensor Network with Charging Delay Mathematics WRSNs stable analysis Hopf bifurcation optimal control |
| title | Analysis and Control of Malware Mutation Model in Wireless Rechargeable Sensor Network with Charging Delay |
| title_full | Analysis and Control of Malware Mutation Model in Wireless Rechargeable Sensor Network with Charging Delay |
| title_fullStr | Analysis and Control of Malware Mutation Model in Wireless Rechargeable Sensor Network with Charging Delay |
| title_full_unstemmed | Analysis and Control of Malware Mutation Model in Wireless Rechargeable Sensor Network with Charging Delay |
| title_short | Analysis and Control of Malware Mutation Model in Wireless Rechargeable Sensor Network with Charging Delay |
| title_sort | analysis and control of malware mutation model in wireless rechargeable sensor network with charging delay |
| topic | WRSNs stable analysis Hopf bifurcation optimal control |
| url | https://www.mdpi.com/2227-7390/10/14/2376 |
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