Research on the entropy of logistic chaos

Pan Xin-Yu; Zhao He-Ming

doi:10.7498/aps.61.200504

Abstract

As a simple one-dimensional chaotic system, logistic map has some important applications in many fields. The stable entropy characteristic of logistic function is proposed in this paper. A series of logistic sequence entropy, calculated under different initial values and values of parameter μ, is found to have some special distributions. A great number of numerical simulations prove that the entropy is determined by parameter μ, and it is irrelevant with initial value. The logistic sequence becomes a uniform distribution, and its entropy is close to a maximum, when μ is increased to 4. Thereby the stationary quality of logistic chaos can be speculated to some extent.

Keywords:

logistic system /
chaos /
entropy

Authors and contacts

Pan Xin-Yu^{1 2},
Zhao He-Ming²

1.
School of Electronics and Information Engineering, University of Science and Technology of Suzhou, Suzhou 215011, China;
2.
School of Electronics and Information Engineering, Soochow University, Suzhou 215021, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61071215), the Postgraduate Research Innovation Project of Jiangsu Province, China (Grant No. CXZZ12_0815), and the Fundamental Research and Application Foundation of Suzhou, China (Grant No. SYG201033).

References

[1]	Wang X Y, Qin X 2012 Math. Probl. Eng. 2012 601309
[2]	Wang X Y, Wang M J 2007 Chaos 17 033106
[3]	Feigenbaum M J 1978 J. Stat. Phys. 19 25
[4]	Tang J S, Ouyang K J 2006 Acta Phys. Sin. 55 4437 (in Chinese) [唐驾时, 欧阳克俭 2006 物理学报 55 4437]
[5]	Yang L J 2011 Acta Phys. Sin. 60 050502 (in Chinese) [杨林静 2011 物理学报 60 050502]
[6]	Stein R R, Isambert H 2011 Phys. Rev. E 84 051904
[7]	Wang X Y, Liang Q Y 2008 Commun. Nonlinear Sci. 13 913
[8]	Wang X Y, Luo C 2008 Int. J. Mod. Phys. B 22 4275
[9]	Wang X Y, Liang Q Y, Meng J 2008 Int. J. Mod. Phys. C 19 1389
[10]	Peng H P, Li L X, Yang Y X, Zhang X H, Gao Y 2007 Acta Phys. Sin. 56 6245 (in Chinese) [彭海朋, 李丽香, 杨义先, 张小红, 高洋 2007 物理学报 56 6245]
[11]	Wang M J, Wang X Y 2009 Acta Phys. Sin. 58 1467 (in Chinese) [王明军, 王兴元 2009 物理学报 58 1467]
[12]	Zheng H Z, Hu J F, Liu L D, He Z S 2011 Acta Phys. Sin. 60 110507 (in Chinese) [郑皓洲, 胡进峰, 刘立东, 何子述 2011 物理学报 60 110507]
[13]	Gyorgyi G, Szepfalusy P 1985 Phys. Rev. A 31 3477
[14]	Lesne A, Blanc J L, Pezard L 2009 Phys. Rev. E 79 046208
[15]	Luo C W 2009 Acta Phys. Sin. 58 3788 (in Chinese) [罗传文 2009 物理学报 58 3788]

Cited By

[1]	Wang X Y, Qin X 2012 Math. Probl. Eng. 2012 601309
[2]	Wang X Y, Wang M J 2007 Chaos 17 033106
[3]	Feigenbaum M J 1978 J. Stat. Phys. 19 25
[4]	Tang J S, Ouyang K J 2006 Acta Phys. Sin. 55 4437 (in Chinese) [唐驾时, 欧阳克俭 2006 物理学报 55 4437]
[5]	Yang L J 2011 Acta Phys. Sin. 60 050502 (in Chinese) [杨林静 2011 物理学报 60 050502]
[6]	Stein R R, Isambert H 2011 Phys. Rev. E 84 051904
[7]	Wang X Y, Liang Q Y 2008 Commun. Nonlinear Sci. 13 913
[8]	Wang X Y, Luo C 2008 Int. J. Mod. Phys. B 22 4275
[9]	Wang X Y, Liang Q Y, Meng J 2008 Int. J. Mod. Phys. C 19 1389
[10]	Peng H P, Li L X, Yang Y X, Zhang X H, Gao Y 2007 Acta Phys. Sin. 56 6245 (in Chinese) [彭海朋, 李丽香, 杨义先, 张小红, 高洋 2007 物理学报 56 6245]
[11]	Wang M J, Wang X Y 2009 Acta Phys. Sin. 58 1467 (in Chinese) [王明军, 王兴元 2009 物理学报 58 1467]
[12]	Zheng H Z, Hu J F, Liu L D, He Z S 2011 Acta Phys. Sin. 60 110507 (in Chinese) [郑皓洲, 胡进峰, 刘立东, 何子述 2011 物理学报 60 110507]
[13]	Gyorgyi G, Szepfalusy P 1985 Phys. Rev. A 31 3477
[14]	Lesne A, Blanc J L, Pezard L 2009 Phys. Rev. E 79 046208
[15]	Luo C W 2009 Acta Phys. Sin. 58 3788 (in Chinese) [罗传文 2009 物理学报 58 3788]

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