Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application
Yong-Bing Hu(胡永兵)1, Xiao-Min Yang(杨晓敏)1, Da-Wei Ding(丁大为)1,2,†, and Zong-Li Yang(杨宗立)1
1 School of Electronics and Information Engineering, Anhui University, Hefei 230601, China; 2 National Engineering Research Center for Agro-Ecological Big Data Analysis&Application, Anhui University, Hefei 230601, China
Abstract Multi-link networks are universal in the real world such as relationship networks, transportation networks, and communication networks. It is significant to investigate the synchronization of the network with multi-link. In this paper, considering the complex network with uncertain parameters, new adaptive controller and update laws are proposed to ensure that complex-valued multilink network realizes finite-time complex projective synchronization (FTCPS). In addition, based on fractional-order Lyapunov functional method and finite-time stability theory, the criteria of FTCPS are derived and synchronization time is given which is associated with fractional order and control parameters. Meanwhile, numerical example is given to verify the validity of proposed finite-time complex projection strategy and analyze the relationship between synchronization time and fractional order and control parameters. Finally, the network is applied to image encryption, and the security analysis is carried out to verify the correctness of this method.
Yong-Bing Hu(胡永兵), Xiao-Min Yang(杨晓敏), Da-Wei Ding(丁大为), and Zong-Li Yang(杨宗立) Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application 2022 Chin. Phys. B 31 110501
[1] Zhao H, Li L X, Xiao J H, Yang Y X and Zheng M W 2017 Chaos, Solitons and Fractals104 268 [2] Zhao H, Li L X, Peng H P, Xiao J H and Yang Y X 2015 Eur. Phys. J. B88 45 [3] Zhao H, Li L X, Peng H P, Xiao J H, Yang Y X and Zheng M W 2016 Nonlinear Dyn.83 1437 [4] Hu Q Y, Peng H P, Wang Y G, Hu Z R and Yang Y X 2012 Nonlinear Dyn.69 1813 [5] Xu Y, Wang Q, Li W X and Feng J Q 2021 Mathematical Methods in the Applied Sciences44 3356 [6] Peng H P, Wei N, Li L X, Xie W S and Yang Y X 2010 Phys. Lett. A374 2335 [7] Li L X, Kurths J, Peng H P, Yang Y X and Luo Q 2013 Eur. Phys. J. B86 125 [8] Wang X and Miao P 2020 Int. J. Control Autom. Syst.18 1993 [9] Li L X, Li W W, Kurths J, Luo Q, Yang Y X and Li S D 2015 Chaos, Solitons and Fractals72 20 [10] Li K Z, He E, Zeng Z R and Tse C K 2013 Chin. Phys. B22 070504 [11] Wang S G and Yao H X 2012 Chin. Phys. B21 050508 [12] Aadhithiyan S, Raja R, Zhu Q X and Alzabut J 2021 Neural Process. Lett.53 1035 [13] Wang J Y, Zhang H G, Wang Z S and Liang H J 2013 Chin. Phys. B22 090504 [14] Sha H S, Wang G J, Hao T and Wang Z X 2020 Complexity2020 3742876 [15] Ding D W, Yao X L and Zhang H W 2020 Neural Process. Lett.51 325 [16] Yang X S and Cao J D 2010 Appl. Math. Model.34 3631 [17] Li J R, Jiang H J, Hu C and Yu J 2018 Chaos, Solitons and Fractals114 291 [18] Wang W P, Peng H P, Li L X, Xiao J H and Yang Y X 2015 Neural Process. Lett.41 71 [19] Zhao H, Li L X, Peng H P, Xiao J H, Yang Y X and Zheng M W 2017 Modern Phys. Lett. B31 1750008 [20] Zheng M W, Li L X, Peng H P, Xiao J H, Yang Y X, Zhang Y P and Zhao H 2019 Commun. Nonlinear Sci. Numer. Simulat.67 108 [21] Li H L, Cao J D, Hu C, Zhang L and Wang Z L 2019 Neurocomputing356 31 [22] Bao H B, Park J H and Cao J D 2021 IEEE Transactions on Neural Networks and Learning Systems32 3230 [23] Ding D W, Yan J, Wang N and Liang D 2017 Commun. Theor. Phys.68 366 [24] Ding D W, Yan J, Wang N and Liang D 2017 Chaos, Solitons and Fractals104 41 [25] Yang S, Yu J, Hu C and Jiang H J 2018 Neural Networks104 104 [26] Xu Y, Li Y Z and Li W X 2020 Commun. Nonlinear Sci. Numer. Simulat.85 105239 [27] Yang X S and Cao J D 2014 Appl. Math. Comput.227 480 [28] Banu L J and Balasubramaniam P 2016 Neurocomputing179 126 [29] Zhang C, Wang X Y, Luo C, Li J Q and Wang C P 2018 Physica A494 251 [30] Wu Z Y, Liu D F and Ye Q L 2015 Commun. Nonlinear Sci. Numer. Simulat.20 273 [31] Li H L, Cao J D, Jiang H J and Alsaedi A 2019 Physica A533 122027 [32] Du L, Yang Y and Lei Y M 2018 Appl. Math. Mech.-Engl. Ed.39 353 [33] Yang X Y, Li X D and Duan P Y 2022 Neural Comput. Appl.34 5097 [34] Zhang L M, Sun K H, Liu W H and He S B 2017 Chin. Phys. B26 100504 [35] Wang Y Z and Yang F F 2021 Phys. Scr.96 035209 [36] Kumar M, lqbal A and Kumar P 2016 Signal Process.125 187 [37] Chai X L, Gan Z H, Yuan K, Chen Y R and Liu X X 2019 Neural Comput. Appl.31 219 [38] Xu Y and Li W X 2020 Physica A549 123903 [39] Wu Z Y and Fu X C 2013 Nonlinear Dyn.72 9 [40] Xu Q, Zhuang S X, Liu S J and Xiao J 2016 Neurocomputing186 119 [41] Ding D W, Yao X L and Wang N 2019 Int. J. Theor. Phys.58 2357 [42] Ji G J, Hu C, Yu J and Jiang H J 2018 J. Frankl. Inst.355 4665 [43] Li H L, Cao J D, Jiang H J and Alsaedi A 2018 J. Frankl. Inst.355 5771
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
