Based on the Lyapunov stability theory, the theoretical analysis shows that under appropriate conditions, the drive-response network can achieve global synchronization through adaptive pinning control method. This method is more general and convenient. At the same time, this paper designs a secure communication system based on chaotic masking technology, which can realize one-to-many real-time transmission of information, and has the characteristics of fast decryption speed and high security. Finally, the correctness of the theoretical results is verified by numerical simulation.
ZHU Xiaojing
,
LI Kezan
,
DING Yong
,
ZHU Xiaojing
,
LI Kezan
,
DING Yong
. Successive Projective Synchronization and Its Application in Secure Communication[J]. Complex Systems and Complexity Science, 2022
, 19(1)
: 27
-33
.
DOI: 10.13306/j.1672-3813.2022.01.004
[1] GU Y Q, HUANG W Q, CHEN T L. Chaotic dynamics in weight space of neural networks[J]. Communications in Theoretical Physics, 1999, 32(2): 247-252.
[2] XU D L, LI Z, BISHOP S R. Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems[J]. Chaos, 2001, 11(3): 439-442.
[3] ARIANOS S, BOMPARD E, CARBONE A, et al. Power grid vulnerability: a complex network approach[J]. Chaos, 2009, 19(1): 013119.
[4] MUKHERJEE J, RAMAMURTHY B. Communication technologies and architectures for space network and interplanetary internet[J]. IEEE Communications Surveys and Tutorials, 2013, 15(2): 881-897.
[5] CHEE C Y, XU D. Chaos-based m-ary digital communication technique using controlled projective synchronisation[J]. IEE Proceedings-Circuits Devices and Systems, 2006, 153(4): 357-360.
[6] DUA H Y, ZENG Q S, WANG C H, et al. Function projective synchronization in coupled chaotic systems[J]. Nonlinear Analysis: Real World Applications, 2010,11(2): 705-712.
[7] 陆君安. 复杂网络的同步和拓扑结构的识别[J]. 复杂系统与复杂性科学, 2010, 7(2): 19-23.
[8] 汪小帆, 李翔, 陈关荣. 网络科学导论[M]. 北京: 高等教育出版社, 2012.
[9] 陈天平, 卢文联. 复杂网络协调性理论[M]. 北京: 高等教育出版社, 2013.
[10] 张新建, 韦爱举, 李科赞. 具有通信时延的动态网络的相继滞后同步[J]. 中国物理B, 2016, 25(3): 038901.
ZHANG X J, WEI A J, LI K Z. Successive lag synchronization on dynamical networks with communication delay[J]. Chinese Physics B, 2016, 25(3): 038901.
[11] CHEN J, JIAO L, WU J, et al. Projective synchronization with different scale factors in a driven-response complex network and its application in image encryption[J]. Nonlinear Analysis: Real World Applications, 2010, 11(4): 3045-3058.
[12] HSIAO F H. Fuzzy control of dithered chaotic systems via neural-network-based approach[J]. Journal of the Franklin Institute, 2010, 347(7): 1114-1136.
[13] HU G, XIAO J H, GAO J, et al. Analytic study of spatiotemporal chaos control by applying local injections[J]. Physical Review E, 2000, 62(3): 3043-3047.
[14] PAREKH N, PARTHASARATHY S, SINHA S. Global and local control of spatiotemporal chaos in coupled map lattices[J]. Physical Review Letters, 1998, 81(7): 1401-1404.
[15] MAHMOUD G M, ALY S A, FARGHALY A A. On chaos synchronization of a complex two coupled dynamos system[J]. Chaos Solitons and Fractals, 2007, 33(1): 178-187.
[16] 陈关荣. 控制非线性动力系统的混沌现象[J]. 控制理论与应用,1997, 1997(1): 1-6.
CHEN G R. Controlling chaos in nonlinear dynamical systems[J]. Control Theory and Applications, 1997, 1997 (1): 1-6.
[17] PESENSON M Z, PESENSON I Z. Adaptive multiresolution analysis based on synchronization[J]. Physical Review E, 2011, 84(4): 045202.
[18] ZHANG Y X, LI K Z. Successive lag synchronization on nonlinear dynamical networks via aperiodically intermittent control[J]. Nonlinear Dynamics, 2019, 95(4): 3075-3089.
[19] TONG D B, ZHOU W N, ZHOU X H, et al. Exponential synchronization for stochastic neural networks with multi-delayed and Markovian switching via adaptive feedback control[J]. Communications in Nonlinear Science and Numerical Simulation, 2015, 29(1/3): 359-371.
[20] HU M F, YANG Y Q, XU Z Y, et al. Projective synchronization in drive-response dynamical networks[J]. Physica A, 2007, 381(1): 457-466.
[21] ZHENG S, BI Q S, CAI G L. Adaptive projective synchronization in complex networks with time-varying coupling delay[J]. Physics Letters A, 2009, 373(17): 1553-1559.
[22] XU D L, LI Z G. Controlled projective synchronization in nonpartially-linear chaotic systems[J]. International Journal of Bifurcation and Chaos, 2002, 12(6): 1395-1402.
[23] CAI N, JING Y W, ZHANG S Y. Modified projective synchronization of chaotic systems with disturbances via active sliding mode control[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(6): 1613-1620.
[24] CHEN Y, LI X. Function projective synchronization between two identical chaotic systems[J]. International Journal of Modern Physics C, 2007, 18(5): 883-888.
[25] SUN M, ZENG C Y, TIAN L X. Projective synchronization in drive-response dynamical networks of partially linear systems with time-varying coupling delay[J]. Physics Letters A, 2008, 372(46): 6904-6908.
[26] HU M F, XU Z Y. Adaptive feedback controller for projective synchronization[J]. Nonlinear Analysis: Real World Applications, 2008, 9(3): 1253-1260.
[27] 祝晓静, 李科赞, 丁勇. 复杂动力学网络上的基于线性控制下的相继投影同步,桂林电子科技大学学报, 2021, 41(6):510-515.
ZHU X J, LI K Z, DING Y. Successive projective synchronization based on linear control over complex dynamical networks[J]. Journal of Guilin University of Electronic Technology, 2021, 41(6):510-515.
[28] LI D M, LU J, WU X Q, et al. Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system[J]. Journal of Mathematical Analysis and Applications, 2006, 323(2): 844-853.
[29] HORN R A, JOHNSON C R. Matrix analysis, Second Edition[M]. New York: Cambridge University Press, 2013.
