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Chin. Phys. B, 2019, Vol. 28(2): 020503    DOI: 10.1088/1674-1056/28/2/020503
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Design new chaotic maps based on dimension expansion

Abdulaziz O A Alamodi, Kehui Sun(孙克辉), Wei Ai(艾维), Chen Chen(陈晨), Dong Peng(彭冬)
School of Physics and Electronics, Central South University, Changsha 410083, China
Abstract  Based on the high-dimensional (HD) chaotic maps and the sine function, a new methodology of designing new chaotic maps using dimension expansion is proposed. This method accepts N dimensions of any existing HD chaotic map as inputs to generate new dimensions based on the combined results of those inputs. The main principle of the proposed method is to combine the results of the input dimensions, and then performs a sine-transformation on them to generate new dimensions. The characteristics of the generated dimensions are totally different compared to the input dimensions. Thus, both of the generated dimensions and the input dimensions are used to create a new HD chaotic map. An example is illustrated using one of the existing HD chaotic maps. Results show that the generated dimensions have better chaotic performance and higher complexity compared to the input dimensions. Results also show that, in the most cases, the generated dimensions can obtain robust chaos which makes them attractive to usage in a different practical application.
Keywords:  chaos      sine-transform      dimension expansion      permutation entropy  
Received:  01 November 2018      Revised:  16 December 2018      Accepted manuscript online: 
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Jn (High-dimensional chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61161006 and 61573383).
Corresponding Authors:  Kehui Sun     E-mail:  kehui@scu.edu.cn

Cite this article: 

Abdulaziz O A Alamodi, Kehui Sun(孙克辉), Wei Ai(艾维), Chen Chen(陈晨), Dong Peng(彭冬) Design new chaotic maps based on dimension expansion 2019 Chin. Phys. B 28 020503

[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Jian L H and Zhang J S 2010 Chin. Phys. B 19 050508
[3] Chai X L, Gan Z H, Lu Y, Zhang M H and Chen Y R 2016 Chin. Phys. B 25 100503
[4] Yang T, Wu C W and Chua L O 1997 IEEE Trans. Circuits Syst. I 44 469
[5] Mu J, Tao C and Du G H 2003 Chin. Phys. B 12 381
[6] Peng R H and Chao B 2015 Chin. Phys. B 24 080503
[7] Reyad O and Kotulski Z 2015 Appl. Math. Inf. Sci. 9 31
[8] Yu M Y, Sun K H, Liu W H and He S B 2018 Chaos, Solitons and Fractals 106 107
[9] Ling C, Wu X F and Sun S G 1999 IEEE Trans. Signal Process. 47 1424
[10] Wu X G, Hu H P and Zhang B L 2004 Chaos, Solitons and Fractals 22 359
[11] Arroyo D, Diaz J and Rodriguez F B 2013 Signal Process. 93 1358
[12] Li C Q, Zhang L Y, Ou R, Wong K and Shu S 2012 Nonlinear Dyn. 70 2383
[13] Skrobek A 2007 Phys. Lett. A 363 84
[14] Hénon M 1976 Commun. Math. Phys. 50 69
[15] Liu W H, Sun K H and He S B 2017 Nonlinear Dyn. 89 2521
[16] Rössler O E 1979 Phys. Lett. A 71 155
[17] Hua Z Y, Zhou B H and Zhou Y C 2017 IEEE Trans. Industr. Electron. 65 2557
[18] Sheng L Y, Sun K H and Li C B 2004 Acta Phys. Sin. 53 2871 (in Chinese)
[19] Wang G Y and Yuan F 2013 Acta Phys. Sin. 62 020506 (in Chinese)
[20] Zhou Y, Hua Z, Pun C M and Chen C L P 2014 IEEE Trans. Cybern. 45 2001
[21] Li J H and Liu H 2013 IET Inform. Secur. 7 265
[22] Wu Y, Noonan J P, Yang G and Jin H 2012 J. Electron. Imag. 21 013014
[23] Hua Z Y, Zhou Y C, Pun C M and Philip Chen C L 2015 Inform. Sci. 297 80
[24] Chen G R, Mao Y B and Chui C K 2004 Chaos, Solitons and Fractals 21 749
[25] Singh J P, Pham V T, Hayat T, Jafari S, Alsaadi F E and Roy B K 2018 Chin. Phys. B 27 100501
[26] Shen C W, Yu S M, Lü J H and Chen G R 2014 IEEE Trans. Circuits and Syst. 61 2380
[27] Hua. Z Y and Zhou Y C 2016 Inform. Sci. 339 237
[28] Banerjee S, Yorke J A and Grebogi C 1998 Phys. Rev. Lett. 80 3049
[29] Glendinning P 2017 Eur. Phys. J. Spec. Top. 226 1721
[30] Andrecut M and Ali M K 2001 Europhys. Lett. 54 300
[31] Zeraoulia E and Sprott J C 2011 Robust Chaos and its Applications (Singapore: World Scientific) pp. 27-38
[32] Skokos C 2009 The Lyapunov Characteristic Exponents Their Computation (Heidelberg: Springer-Berlin) pp. 64-74
[33] Linh V H, Mehrmann V and Van Velks E S 2011 Adv. Comput. Math. 35 281
[34] Bandt C and Pompe B 2002 Phys. Rev. Lett. 88 174102
[35] Grassberger P and Procaccia I 1983 Phys. Rev. A 28 2591
[36] Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297
[37] Chen W, Zhang J, Yu W X and Wang Z Z 2009 Med. Eng. Phys. 31 61
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