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Ever since the special characteristics hidden in the chaos was discovered, the chaotic behavior has been extensively studied as a ubiquitous and complex nonlinear dynamic phenomenon, which is gradually extending to various disciplines of natural and social science, and the significant values in the theoretical and the practical application have attracted much attention from scholars of different fields in the recent decades. Conventional methods of analyzing chaotic dynamic systems, including the Lyapunov exponent, correlation dimension, Poincar map, unavoidably encounter some common problems, such as reconstruction of the phase space, determination of the linear area, etc. Besides, the current approaches each also possess a poor capability of balancing the direct observation and the quantitative calculation. Based on the fact that the neighbor data relate to each other to some degree, taking those shortages into consideration, aiming at depicting the chaotic features efficiently, a new method of analyzing the complicated chaotic motion is proposed. During the processing of that novel approach, the Euclidean distance is continuously computed to represent the dependence of the adjacent unit, after that, the original complicated array is converted into a simpler series composed of the distance of neighbor sub-sequences with more distinct characteristics. The mean value and the standard deviation of the newborn series are exacted to assist in describing the chaotic changing law. The method is adopted for studying the typical chaotic models, like Logistic model, Chebychev model, Duffing oscillator, Lorenz system, etc., which proves the good performances in explaining the chaotic variation rules in different systems. Based on the model verification, it could be seen that the method could detect the chaotic motion both qualitatively and quantitatively, and the ability for that method to resist the noise is improved up to some degree, what is more, the information about the real model is not required, thereby simplifying the analysis of the complicated chaotic behavior whose authentic model is unavailable. In addition, the method is applied to decomposing the vibration signal to monitor the working condition of the rotating rotor, and the results show that the conditional variation could be detected obviously. The analyses above show that the proposed method, on the basis of the dependence between nearby data, could perform well in observing the chaotic feature in an efficient way which simplifies the operation and clarifies the chaotic variation, moreover, the application potential of this method is worthy of great attention.
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Keywords:
- chaos /
- nonlinear /
- dependence /
- distance of neighbor sub-sequences
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[31] Li C B, Sprott J C, Thio W 2015 Phys. Lett. A 379 888
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[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Zhang X D, Liu X D, Zheng Y, Liu C 2013 Chin.Phys.B 22 030509
[3] Hossein G, Amir H, Azita A 2013 Chin.Phys.B 22 010503
[4] Coelho A L V, Lima C A M 2014 Eng. Appl. Artif. Intel. 36 81
[5] Varney P, Green I 2015 J. Sound Vib. 336 207
[6] Krese B, Govekar E 2013 Transport. Res. C 36 27
[7] Wang J S, Yuan R X, Gao Z W, Wang D J 2011 Chin. Phys. B 20 090506
[8] Mohammad Z K, Ozgur K 2015 Ocean Eng. 100 46
[9] Jin W L 2013 Transport. Res. B 57 191
[10] Sun K H, Yang J L, Ding J F, Sheng L Y 2010 Acta Phys. Sin. 59 8385 (in Chinese) [孙克辉, 杨静利, 丁家峰, 盛利元 2010 物理学报 59 8385]
[11] Kulp C W 2013 Chaos 23 033110
[12] Look N, Arellano C J, Grabowski A M, McDermott W J, Kram R, Bradley E 2013 Chaos 23 043131
[13] Jiang L P, Xu K J, Qin H Q 2007 J. Vib. Shock 26 49 (in Chinese) [江龙平, 徐可君, 秦海勤 2007 振动与冲击 26 49]
[14] Zhang Y 2013 Chin. Phys. B 22 050502
[15] Leung S Y 2013 Chaos 23 043132
[16] Wang J S, Yuan J, Li Q, Yuan R X 2011 Chin. Phys. B 20 050506
[17] Takens F 1981 Dynamical Systems and Turbulence (Berlin: Spring Verlag) 366
[18] Zhang J, Fan Y Y, Li H M, Sun H Y, Jia M 2011 Chin. J. Comput. Phys. 28 469 (in Chinese) [张菁, 樊养余, 李慧敏, 孙恒义, 贾蒙 2011 计算物理 28 469]
[19] Jiang A H, Zhou P, Zhang Y, Hua H X 2015 J. Vib. Shock 34 79 (in Chinese) [蒋爱华, 周璞, 章艺, 华宏星 2015 振动与冲击 34 79]
[20] Zhang S Q, Li X X, Zhang L G, Hu Y T, Li L 2013 Acta Phys. Sin. 62 110506 (in Chinese) [张淑清, 李新新, 张立国, 胡永涛, 李亮 2013 物理学报 62 110506]
[21] Li H, Yang Z, Zhang Y M, Wen B C 2011 Acta Phys. Sin. 60 070512 (in Chinese) [李鹤, 杨周, 张义民, 闻邦椿 2011 物理学报 60 070512]
[22] Kim H S, Eykholt R, Salas J D 1999 Physica D 127 48
[23] Zhang S Q, Zhao Y C, Jia J, Zhang L G, Shangguan H L 2010 Chin. Phys. B 19 060514
[24] Ji C C, Zhu H, Jiang W 2010 Sci. Chin. 55 3069 (in Chinese) [姬翠翠, 朱华, 江炜 2010 中国科学 55 3069]
[25] Gao Z K, Yang Y X, Fang P C, Zou Y, Xia C Y, Du M 2015 Europhys. Lett. 109 30005
[26] Gao Z K, Zhang X W, Jin N D, Donner R V, Marwan N, Kurths J 2013 Europhys. Lett. 103 50004
[27] L L, Li G, Guo L, Meng L, Zou J R, Yang M 2010 Chin. Phys. B 19 080507
[28] May R M 1976 Nature 261 459
[29] Liu Y, Fu C 2006 Control Eng. Chin. 13 377 (in Chinese) [刘严, 付冲 2006 控制工程 13 377]
[30] Tang Y Z, Lou J J, Weng X T, Zhu S J 2014 J. Vib. Shock 33 60 (in Chinese) [唐元璋, 楼京俊, 翁雪涛, 朱石坚 2014 振动与冲击 33 60]
[31] Li C B, Sprott J C, Thio W 2015 Phys. Lett. A 379 888
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