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作为形式上相对较为简单的一维混沌函数, Logistic系统在很多领域有着重要的应用. 本文主要分析了Logistic系统的熵稳定特性,对不同参数μ和系统初值形成的Logistic序列, 进行了统计分类,得到了一系列的熵值,并详细分析了熵的分布情况.数值仿真结果表明, Logistic系统的熵由参数μ决定,而与系统初值基本无关,且当参数μ取值接近上界(μ= 4)时, 序列分布越趋于均匀,熵也接近理论极限值.
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关键词:
- Logistic系统 /
- 混沌 /
- 熵
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
[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 55 4437]
[5] Yang L J 2011 Acta Phys. Sin. 60 050502 (in Chinese) [杨林静 2011 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 56 6245]
[11] Wang M J, Wang X Y 2009 Acta Phys. Sin. 58 1467 (in Chinese) [王明军, 王兴元 2009 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 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 58 3788]
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[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 55 4437]
[5] Yang L J 2011 Acta Phys. Sin. 60 050502 (in Chinese) [杨林静 2011 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 56 6245]
[11] Wang M J, Wang X Y 2009 Acta Phys. Sin. 58 1467 (in Chinese) [王明军, 王兴元 2009 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 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 58 3788]
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