Mechanism analysis of regulating Turing instability and Hopf bifurcation of malware propagation in mobile wireless sensor networks

doi:10.1088/1674-1056/ad24d5

中国物理B ›› 2024, Vol. 33 ›› Issue (6): 60202-060202.doi: 10.1088/1674-1056/ad24d5

Mechanism analysis of regulating Turing instability and Hopf bifurcation of malware propagation in mobile wireless sensor networks

Xi-Xi Huang(黄习习)¹, Min Xiao(肖敏)^1,†, Leszek Rutkowski², Hai-Bo Bao(包海波)³, Xia Huang(黄霞)³, and Jin-De Cao(曹进德)⁴

1 College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
2 Systems Research Institute of the Polish Academy of Sciences, 01-447 Warsaw, Poland;
3 College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China;
4 School of Mathematics, Southeast University, Nanjing 210096, China

收稿日期:2023-11-09 修回日期:2024-01-19 接受日期:2024-02-01 出版日期:2024-06-18 发布日期:2024-06-18
通讯作者: Min Xiao E-mail:candymanxm2003@aliyun.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 62073172) and the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20221329).

Mechanism analysis of regulating Turing instability and Hopf bifurcation of malware propagation in mobile wireless sensor networks

Xi-Xi Huang(黄习习)¹, Min Xiao(肖敏)^1,†, Leszek Rutkowski², Hai-Bo Bao(包海波)³, Xia Huang(黄霞)³, and Jin-De Cao(曹进德)⁴

1 College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
2 Systems Research Institute of the Polish Academy of Sciences, 01-447 Warsaw, Poland;
3 College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China;
4 School of Mathematics, Southeast University, Nanjing 210096, China

Received:2023-11-09 Revised:2024-01-19 Accepted:2024-02-01 Online:2024-06-18 Published:2024-06-18
Contact: Min Xiao E-mail:candymanxm2003@aliyun.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 62073172) and the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20221329).

摘要/Abstract

摘要： A dynamical model is constructed to depict the spatial-temporal evolution of malware in mobile wireless sensor networks (MWSNs). Based on such a model, we design a hybrid control scheme combining parameter perturbation and state feedback to effectively manipulate the spatiotemporal dynamics of malware propagation. The hybrid control can not only suppress the Turing instability caused by diffusion factor but can also adjust the occurrence of Hopf bifurcation induced by time delay. Numerical simulation results show that the hybrid control strategy can efficiently manipulate the transmission dynamics to achieve our expected desired properties, thus reducing the harm of malware propagation to MWSNs.

关键词: mobile wireless sensor networks, reaction-diffusion, Hopf bifurcation, hybrid control

Abstract: A dynamical model is constructed to depict the spatial-temporal evolution of malware in mobile wireless sensor networks (MWSNs). Based on such a model, we design a hybrid control scheme combining parameter perturbation and state feedback to effectively manipulate the spatiotemporal dynamics of malware propagation. The hybrid control can not only suppress the Turing instability caused by diffusion factor but can also adjust the occurrence of Hopf bifurcation induced by time delay. Numerical simulation results show that the hybrid control strategy can efficiently manipulate the transmission dynamics to achieve our expected desired properties, thus reducing the harm of malware propagation to MWSNs.

Key words: mobile wireless sensor networks, reaction-diffusion, Hopf bifurcation, hybrid control

中图分类号: (Partial differential equations)

02.30.Jr

02.60.Cb (Numerical simulation; solution of equations)

Xi-Xi Huang(黄习习), Min Xiao(肖敏), Leszek Rutkowski, Hai-Bo Bao(包海波), Xia Huang(黄霞), and Jin-De Cao(曹进德). Mechanism analysis of regulating Turing instability and Hopf bifurcation of malware propagation in mobile wireless sensor networks[J]. 中国物理B, 2024, 33(6): 60202-060202.

参考文献

[1] Wang Y Q and Yang X Y 2013 Chin. Phys. B 22 010509
[2] Wang Y Q and Yang X Y 2013 Chin. Phys. B 22 040206
[3] Li Y and Liu Y 2005 Chin. Phys. B 14 2153
[4] Li Q, Zhang B H and Cui L G 2012 Chin. Phys. B 21 050205
[5] Feng X, Liu L and Zhang F 2022 Acta Math. Appl. Sin. 38 282
[6] Lu Y L, Jiang G P and Song Y R 2012 Chin. Phys. B 21 100207
[7] Ren J, Yang X and Zhu Q 2012 Nonlinear Anal. Real World Appl. 13 376
[8] Chong Y, Kashyap A J and Chen S 2023 Axioms 12 1031
[9] Abdelouahab M S, Arama A and Lozi R 2021 Chaos 31 123125
[10] Zhang Z and Bi D 2016 Discrete Dyn. Nat. Soc. 2016 3067872
[11] ao Y, Fu Q, Yang W, Wang Y and Sheng C 2018 Secur. Commun. Netw. 2018 9756982
[12] Du Y, Niu B and Wei J 2022 Acta Math. Appl. Sin. 38 128
[13] Kumari S and Upadhyay R K 2021 Math. Comput. Simul. 190 246
[14] Yu S, Yu Z and Jiang H 2021 Inf. Sci. 581 18
[15] Lu L, Huang C and Song X 2023 Eur. Phys. J. Plus 138 77
[16] Khan A Q, Bukhari S A H and Almatrafi M B 2022 Alex. Eng. J. 61 11391
[17] Zhu L, Zhao H and Wang X 2015 Commun. Nonlinear Sci. Numer. Simul. 22 747
[18] Mao Z S, Wang H, Xu D D and Cui Z J 2013 Math. Probl. Eng. 2013 315367
[19] Zhou W G 2018 Physica A 515 183
[20] Feng L P, Song L P, Zhao Q S and Wang H B 2015 Math. Probl. Eng. 2015 129598
[21] Zhang Z Z, Chu Y G, H U, Kumari S and Ranjit K U 2019 Zhejiang Da Xue Xue Bao Li Xue Ban 46 172
[22] Wang X M, He Z B, Zhao X Q, Lin C, Pan Y and Cai Z P 2013 Sci. China Inf. Sci. 56 092303
[23] Ding L, Hu P and Guan Z H 2020 IEEE Trans. Syst. Man Cybern. Syst. 51 6779
[24] Ding D W, Zhang X Y, Wang N and Liang D 2017 J. Shanghai Jiaotong Univ. Sci. 22 206
[25] Wu Z, Cai Y and Wang Z 2023 J. Differ. Equ. 352 221
[26] Yang R 2022 Chaos Solitons Fractals 164 112659
[27] Wang S, Ding Y and Lu H 2021 Math. Biosci. Eng 18 5505
[28] Golubitsky M and Langford W F 1981 J. Differ. Equ. 41 375
[29] Gbber F and Willamowski K D 1979 J. Math. Anal. Appl. 71 333
[30] Peng M and Zhang Z 2020 J. Vib. Control 26 1232
[31] Gao Q 2009 International Workshop on Chaos-Fractals Theories and Applications, November 6-8, 2009, Shenyang, China, p. 272
[32] Honghua B, Daifeng D and Junjie W 2023 Math. Biosci. Eng. 20 12194
[33] Liu J and Zhang Z 2019 Adv. Differ. Equ. 2019 442
[34] Hsu L and Favretto L 1984 J. Math. Anal. Appl. 101 562
[35] Zeng X, Xiong Z and Wang C 2016 Appl. Math. Comput. 282 17
[36] Chen Y Y and Bi Y Q 2014 J. Appl. Math. 2014 804204
[37] Song L Y, He Y N and Ge Z H 2007 Appl. Math. Comput. 190 677

Mechanism analysis of regulating Turing instability and Hopf bifurcation of malware propagation in mobile wireless sensor networks

Mechanism analysis of regulating Turing instability and Hopf bifurcation of malware propagation in mobile wireless sensor networks

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	Wen-Huan Ai(艾文欢), Zheng-Qing Lei(雷正清), Dan-Yang Li(李丹洋), Dong-Liang Fang(方栋梁), and Da-Wei Liu(刘大为). Bifurcation analysis and control study of improved full-speed differential model in connected vehicle environment[J]. 中国物理B, 2024, 33(7): 70503-070503.
[2]	Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军), Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷). Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays[J]. 中国物理B, 2023, 32(3): 38701-038701.
[3]	Tao Wang(王涛) and Tiegang Liu(刘铁钢). Transition to chaos in lid-driven square cavity flow[J]. 中国物理B, 2021, 30(12): 120508-120508.
[4]	王涛, 刘铁钢, 王正. The second Hopf bifurcation in lid-driven square cavity[J]. 中国物理B, 2020, 29(3): 30503-030503.
[5]	张良, 唐驾时, 韩芩. Hopf bifurcation control of a Pan-like chaotic system[J]. 中国物理B, 2018, 27(9): 94702-094702.
[6]	鲍江宏, 陈丹丹. Coexisting hidden attractors in a 4D segmented disc dynamo with one stable equilibrium or a line equilibrium[J]. 中国物理B, 2017, 26(8): 80201-080201.
[7]	Naruemon Rueangkham, Charin Modchang. Computational analysis of the roles of biochemical reactions in anomalous diffusion dynamics[J]. 中国物理B, 2016, 25(4): 48201-048201.
[8]	刘爽, 赵双双, 王兆龙, 李海滨. Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback[J]. , 2015, 24(1): 14501-014501.
[9]	刘爽, 赵双双, 孙宝平, 张文明. Bifurcation and chaos analysis of a nonlinear electromechanical coupling relative rotation system[J]. , 2014, 23(9): 94501-094501.
[10]	竺致文, 张庆昕, 许佳. Nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film-shaped memory alloy composite plate subjected to in-plane stochastic excitation[J]. , 2014, 23(8): 88201-088201.
[11]	贾冰. Synchronization transition of a coupled system composed of neurons with coexisting behaviors near a Hopf bifurcation[J]. 中国物理B, 2014, 23(5): 50510-050510.
[12]	张月, 卓青青, 刘红侠, 马晓华, 郝跃. Flat-roof phenomenon of dynamic equilibrium phase in the negative bias temperature instability effect on a power MOSFET[J]. 中国物理B, 2014, 23(5): 57304-057304.
[13]	陈梦娇, 令恒莉, 刘一辉, 屈世显, 任维. Bifurcation diagram globally underpinning neuronal firing behaviors modified by SK conductance[J]. 中国物理B, 2014, 23(2): 28701-028701.
[14]	张玮亚, 李永丽, 常晓勇, 王楠. Dynamical investigation and parameter stability region analysis of a flywheel energy storage system in charging mode[J]. 中国物理B, 2013, 22(9): 98401-098401.
[15]	薛薇, 齐国元, 沐晶晶, 贾红艳, 郭彦岭. Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system[J]. 中国物理B, 2013, 22(8): 80504-080504.