Potential risk of variable parameter cascade chaos system

Jin Jian-Guo; Di Zhi-Gang; Wei Ming-Jun

doi:10.7498/aps.63.120509

Abstract

Lyapunov index is one of criteria for testing whether the system is in a chaotic state, and its value represents the developed level of system chaotic state. To study the Lyapunov index characteristic of cascade chaotic system and reveal disturbance mechanism among subsystems in cascade chaotic system, the following researches are carried out. First, the disturbance model among subsystems is constructed from the viewpoint of pseudo noise disturbance, Lyapunov index difference between without and with external noise influence is investigated. Then the conclusion that disturbances among subsystems can be considered as pseudo noise influence is drawn. Second, the conclusion is proved that cascade system Lyapunov index is not the algebraic sum of each independent subsystems, but the one of each subsystems which consist of pre disturbances. Then taking the logistic representation for example, nine cascade systems are designed to prove this conclusion. And some novel characteristics and phenomena are found from the above investigations. They are (a) the phenomenon of “more is less”, that is, Lyapunov index will decrease with the increase of cascade levels, and the phenomenon of “A miss is as good as mile”; (b) even each independent subsystems is chaotic, the cascade system needs not to be chaotic; conversely, even each independent subsystems is not chaotic, the cascade system may be chaotic; (c) whether the cascade system is chaotic is associated with the order of subsystem. Finally, it is pointed out that cascade level has the influences of pros and cons on cascade system, thus revealing the latent hazard of parametric cascade chaotic system. The research result can provide important theoretic foundation for system security and the scientific evaluation of encryption keys.

Keywords:

Authors and contacts

1.
College of Sciences, Hebei United University, Tangshan 063009, China;
2.
College of Information Engineering, Hebei United University, Tangshan 063009, China;
3.
College of Electrical Engineering, Hebei United University, Tangshan 063009, China
Funds: Project supported by the Natural Science Foundation of Hebei Province, China (Grant No. F2014209108).

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Cited By

[1]	Alvarez G 2005 Chaos Soliton. Fract. 26 7
[2]	Wang X Y, Teng L 2012 Chin. Phys. B 21 020504
[3]	Tong X J 2013 Commun. Ninlinear Sci. Numer. Simul. 18 1725
[4]	Ahmed A, Abd E, Li L, Wang N, Han Q, Niu X M 2013 Sign. Process. 93 2986
[5]	Jin J X, Qiu S S 2010 Acta Phys. Sin. 59 792 (in Chinese) [晋建秀, 丘水生 2010 物理学报 59 792]
[6]	Zhu C X, Sun K H 2012 Acta Phys. Sin. 61 120503 (in Chinese) [朱从旭, 孙克辉 2012 物理学报 61 120503]
[7]	Yuan Z X, Huang G H 2012 Chin. Phys. B 21 010502
[8]	Wang X Y, He G X 2012 Chin. Phys. B 21 060502
[9]	Luo Y L, Du M H 2013 Chin. Phys. B 22 080503
[10]	Zhang C X, Yu S M 2010 Acta Phys. Sin. 59 3017 (in Chinese) [张朝霞, 禹思敏 2010 物理学报 59 3017]
[11]	Jin J G, Chen C, Wei M J, Xia L C, Di Z G, Jia C R 2012 Comput. Engineer. 38 95 (in Chinese) [金建国, 陈晨, 魏明军,夏丽春, 贾春荣 2012 计算机工程 38 95]
[12]	Li N, Li J F, Liu Y P 2010 Acta Phys. Sin. 59 5954 (in Chinese) [李农, 李建芬, 刘宇平 2010 物理学报 59 5954]
[13]	Hu J F, Guo J B 2008 Acta Phys. Sin. 57 1477 (in Chinese) [胡进峰, 郭静波 2008 物理学报 57 1477]
[14]	Chen Z, Zeng Y C, Fu Z J 2008 Acta Phys. Sin. 57 46 (in Chinese) [陈争, 曾以成, 付志坚 2008 物理学报 57 46]
[15]	Huang F, Guan Z H 2005 Chaos Soliton. Fract. 23 851
[16]	Yao C G, Zhao Q, Yu J 2013 Phys. Lett. A 377 370
[17]	Choi S Y, Lee E K 1995 Phys. Lett. A 205 173
[18]	Wang G Y, Yuan F 2013 Acta Phys. Sin. 62 020506 (in Chinese) [王光义, 袁方 2013 物理学报 62 020506]
[19]	Cao H F, Zhang R X 2012 Acta Phys. Sin. 61 020508 (in Chinese) [曹鹤飞, 张若洵 2012 物理学报 61 020508]
[20]	Jin J G, Lin R, Zhang Q L, Hou G Q, Di Z G, Jia C R 2009 Comput. Engineer. 35 137 (in Chinese) [金建国, 林瑞, 张庆凌, 侯国强, 邸志刚, 贾春荣 2009 计算机工程 35 137]
[21]	Sekikawa M, Inaba N, Tsubouchi T, Aihara K 2012 Physica D 241 1169
[22]	Stachowiak T, Szydlowski M 2011 Physica D 240 1221
[23]	David R, Lai Y C 2000 Phys. Lett. A 270 308
[24]	Zang H Y, Fan X B, Min L Q, Han D D 2012 Acta Phys. Sin. 61 200508 (in Chinese) [臧鸿雁, 范修斌, 闵乐泉, 韩丹丹 2012 物理学报 61 200508]
[25]	Zhou X Y, Qiao X H, Zhu L, Liu S F 2013 Acta Phys. Sin. 62 190504 (in Chinese) [周小勇, 乔晓华, 朱雷, 刘素芬 2013 物理学报 62 190504]
[26]	Shao K Y, Ma Y J, Wang T T, Liu Y H, Yang L, Gao H Y 2013 Acta Phys. Sin. 62 020514 (in Chinese) [邵克勇, 马永晶, 王婷婷, 刘远红, 杨莉, 高宏宇 2013 物理学报 62 020514]
[27]	Jin J G, Wei M J, Di Z G, Xu G L, Jia C R, Zhao H W 2011 Comput. Engineer. 37 12 (in Chinese) [金建国, 魏明军, 邸志刚, 许广利, 贾春荣, 赵宏微 2011 计算机工程 37 12]
[28]	Hao B L 1993 Advanced Series in Nonlinear Science Staring With Parbolas-An Introduction to Chaotic Dynamics (Vol.1) (Shanghai: Shanghai Scientific and Technolgical Education Press) pp122-125 (in Chinese) [郝柏林 1993 从抛物线谈起–-混沌动力学引论 (第一版) (上海: 上海科学技术出版社) 第122–125页]

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Vol. 63, Issue 12 - 2014-06-20

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