Abstract
In this paper, SE algorithm and C0 algorithm were described in detail. The complexity characteristics of Lü chaotic system, Chua chaotic memristive system, Bao hyperchaotic system, Chen hyperchaotic system are analyzed based on SE algorithm and C0 algorithm. We have compared with the dynamical characteristics of four systems by using the conventional dynamic analysis methods and the methods of complexity, the comparative results demonstrate that SE complexity and C0 complexity can reflect the complexity of continuous chaotic systems accurately and effectually. Through the contrast for the complexity characteristics of two continuous chaotic systems and two continuous hyperchaotic systems, we can obtain that the varying trend of SE complexity and C0 complexity have much well coherence, and it provides a dynamical analytical method for the research of chaos theory.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Mou, J., Wang, Z.S., Kang, L.: Synchronous control of unified chaotic system based on stated observer and its application in secure communication. J. Dalian Polytech. Univ. 27(2), 162–166 (2008)
Sun, K.H., Liu, W., Zhang, T.S.: Implementation of a chaos encryption algorithm. J. Comput. Appl. 23(1), 15–17 (2003)
Zhang, Y.C., Wang, S.J., Li, Y.: Detection of encrypted data-flow based on entropy. Comput. Digit. Eng. 42(4), 555–558 (2014)
Chen, W.T., Zhuang, J., Yu, W.X., et al.: Measuring complexity using Fuzzyen, ApEn and Sampen. Med. Eng. Phys. 31(1), 61–68 (2009)
Sun, K.H., He, S.B., Yin, L.Z., et al.: Application of Fuzzyen algorithm to the analysis of complexity of chaotic sequence. Acta Phys. Sin. 61(13), 130507 (2012)
Chen, X.J., Li, Z., Bai, B.M., et al.: A new complexity metric of chaotic pseudorandom sequences based on Fuzzy entropy. J. Electron. Inf. Technol. 33(5), 1198–1203 (2011)
Sun, K.H., He, S.B., Sheng, L.Y.: Complexity analysis of chaotic sequence based on the intensive statistical complexity algorithm. Acta Phys. Sin. 60(2), 2406–2411 (2011)
Larrondo, H.A., Gonzalez, C.M., Martin, M.T., et al.: Intensive statistical complexity measure of pseudorandom number generators. Phys. Stat. Mech. Appl. 356(1), 133–138 (2005)
Kolmogorov, A.N.: Three approaches for defining the concept of information quantity. Prob. Inf. Transm. 1(1), 3–11 (1965)
Lempel, A., Ziv, J.: On the complexity of finite sequence. IEEE Trans. Inf. Theory 22(1), 75–81 (1976)
Eviatar, H., Somorjai, R.L.: A fast, simple active contour algorithm for biomedical images. Pattern Recogn. Lett. 17(9), 969–974 (1996)
Gneiting, T., Raftery, A.E.: Weather forecasting with ensemble methods. Science 310(5746), 248–249 (2005)
Liao, X.F., Yue, B., Zhou, Q., et al.: A field programmable gate array implementation of an image encryption algorithm based on a discrete chaotic map. J. Chongqing Univ. 31(10), 1189–1193 (2008)
Pincus, S.M.: Approximate entropy (ApEn) as a complexity measure. Chaos 5(1), 110–117 (1995)
Bant, C., Pompe, B.: Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88(17), 1741–1743 (2002)
Lü, J.H., Chen, G.R.: A new chaotic attractor coined. Int. J. Bifurcat. Chaos 12(3), 659–661 (2011)
Bao, B.C., Liu, Z., Xu, J.P.: Dynamical analysis of memristor chaotic oscillator. Acta Phys. Sin. 59(6), 3785–3793 (2010)
Bao, B.C., Liu, Z., Xu, J.P.: New chaotic system and its hyperchaos generation. Syst. Eng. Electron. 20(6), 1179–1187 (2009)
Li, Y.X., Tang, W.K.S., Chen, G.R.: Generating hyperchaos via state feedback control. Int. J. Bifurcat. Chaos 15(10), 3367–3375 (2011)
Sun, K.H., He, S.B., He, Y., Yin, L.Z.: Complexity analysis of chaotic pseudo-random sequences based on spectral entropy algorithm. Acta Phys. Sin. 62(1), 709–712 (2013)
Staniczenko, P.P.A., Lee, C.F., Jones, N.S.: Rapidly detecting disorder in rhythmic biological signals: a spectral entropy measure to identify cardiac arrhythmias. Phys. Rev. Stat. Nonlinear Soft Matter Phys. 79(1), 100–115 (2009)
Dong, Y.Q., Tan, G.Q., Sun, K.H., He, S.B.: Applications of spectral entropy and wavelet entropy algorithm for structure complexity analysis of chaotic sequence. J. Chin. Comput. Syst. 35(2), 348–352 (2014)
Chen, F., Xu, J.H., Gu, F.J., et al.: Dynamic process of information transmission complexity in humaxbrains. Biol. Cybern. 83(4), 355–366 (2000)
Cai, Z.J., Sun, J.: Modified C0 complexity and application. J. Fudan Univ. 47(6), 791–796 (2008)
Sun, K.H., He, S.B., Zhu, C.X., He, Y.: Analysis of chaotic complexity characteristics based on C0 algorithm. Tien Tzu HsuehPao/Acta Electronica Sin. 41(9), 1765–1771 (2013)
Acknowledgements
This work supported by the Provincial Natural Science Foundation of Liaoning (Grant Nos. 20170540060 and 2015020031), Science and Technology Project of Dalian, China (2015A11GX011).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering
About this paper
Cite this paper
Ye, X., Mou, J., Wang, Z., Li, P., Luo, C. (2018). Dynamic Characteristic Analysis for Complexity of Continuous Chaotic Systems Based on the Algorithms of SE Complexity and C0 Complexity. In: Gu, X., Liu, G., Li, B. (eds) Machine Learning and Intelligent Communications. MLICOM 2017. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 227. Springer, Cham. https://doi.org/10.1007/978-3-319-73447-7_69
Download citation
DOI: https://doi.org/10.1007/978-3-319-73447-7_69
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73446-0
Online ISBN: 978-3-319-73447-7
eBook Packages: Computer ScienceComputer Science (R0)