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在林木生长Logistic模型中, 引入加性和乘性关联色噪声, 运用统一色噪声近似、刘维方程以及诺维科夫原理, 推导了近似福克-普朗克方程, 分析了相关参数对稳态概率分布函数的影响. 结果表明: 改变乘性色噪声强度D和加性色噪声强度Q均能导致稳态概率分布曲线峰值高度的改变以及峰位置的移动, 对概率密度分布呈现出漂移作用. 但是在D和Q增大的过程中, 稳态概率分布曲线峰位置的移动方向是不同的: D增大时, 峰的位置向左移动; Q增大时, 峰的位置向右移动. 另外, 当λ >0时, 随着|λ|的增大, 稳态概率分布函数峰的位置向右移动, 且峰值的高度变大; 而λλ|的增大, 稳态概率分布函数峰值的高度也变大, 而峰的位置却向左移动.
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关键词:
- 林木生长 /
- Logistic模型 /
- 色噪声 /
- 稳态概率分布
By virtue of Liouville Theorem and unified colored-noise approximation approach, an approximate Fokker-Planck equation for a tree growth Logistic model subjected to cross-correlated colored noises is derived, and the steady-state probability distribution (SPD) function is obtained. The steady-state properties of the Logistic model are analyzed. We find the following: (1) the position of peak of SPD moves toward left side as D increases while the position of the peak moves toward the contrary direction with Q increasing; (2) the peak of SPD becomes narrow and grows in height as |λ| increases, and for the case of λ >0, the position of peak moves toward right as D increases, but it is opposite for the case of λQ increases.[1] Bai C Y, Yan Y, Mei D C 2010 Chin. Phys. B 19 060503
[2] Zheng Z R, Su W H, Su Y 2007 Acta Phys. Sin. 56 6989 (in Chinese) [郑植仁, 苏文辉, 苏艳 2007 56 6989]
[3] Zhang L, Cao L 2011 Commun. Theor. Phys. 55 462
[4] Wang C J, Wei Q, Mei D C. 2007 Modern Phys. Lett. B 21 789
[5] Yu A H 2003 M. S. Dissertation (Nanjing: Nanjing Forestry University) (in Chinese) [余爱华 2003 硕士学位论文 (南京: 南京林业大学)]
[6] Fang C J 2012 J. Hubei Univ. Technol. 27 92 (in Chinese) [方次军 2012 湖北工业大学学报 27 92]
[7] Bie M J, Zhong W R, Chen H D, Li L, Shao Y Z 2009 Acta Phys. Sin. 58 97 (in Chinese) [别梦杰, 钟伟荣, 陈虎弟, 李立, 邵元智 2009 58 97]
[8] Yang J H, Liu X B 2010 Acta Phys. Sin. 59 3727 (in Chinese) [杨建华, 刘先斌 2010 59 3727]
[9] Liu Z H, Zhou Y R, Zhang A Y, Pang X F 2010 Acta Phys. Sin. 59 699 (in Chinese) [刘志宏, 周玉荣, 张安英, 庞小峰 2010 59 699]
[10] Guo Y F, Xu W 2008 Acta Phys. Sin. 57 6081 (in Chinese) [郭永峰, 徐伟 2008 57 6081]
[11] Zhang H Q, Lu L L, Yan X L, Gao P J 2007 Sci. China 37 246 (in Chinese) [张怀强, 卢丽丽, 阎雪岚, 高培基 2007 中国科学 37 246]
[12] Meng X Y 2006 Forest Mensuration (3nd Ed.) (Beijing: China Forestry Publishing House) pp179–201 (in Chinese) [孟宪宇 2006 测树学(第三版)(北京: 中国林业出版社)第179–201页]
[13] Xing F, Yao S K, Li M L 2011 J. Capital Normal Univ. 32 1 (in Chinese) [邢菲, 姚少魁, 李民丽 2011 首都师范大学学报 32 1]
[14] Chen J, Cheng C M 2008 J. Huazhong Normal Univ. 42 207 (in Chinese) [陈俊, 成传明 2008 华中师范大学学报 42 207]
[15] Han L B 2008 Acta Phys. Sin. 2008 57 2699 (in Chinese) [韩立波 2008 57 2699]
[16] Jia Y, Li J R 1996 Phys. Rev. E 53 5786
[17] Wu D J, Cao L, Ke S Z 1994 Phys. Rev. E 50 2496
[18] Kubo R 1963 J. Math. Phys. 4 174
[19] Novikov E A 1919 Zh. Eksp. Teor. Fiz. 20 1290
[20] Peter J, Peter H 1987 Phys. Rev. A 35 4464
[21] Hu G 1994 Stochastic Forces and Nonlinear System (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) [胡岗 1994 随机力与非线性系统(上海: 上海科技教育出版社)]
[22] Wang C J, Wei Q, Zheng B B, Mei D C 2008 Acta Phys. Sin. 57 1375 (in Chinese) [王参军, 魏群, 郑宝兵, 梅冬成 2008 57 1375]
[23] Nie L R, Mei D C 2007 Phys. Lett. A 371 111
[24] Zhang Y D, Bai S B 2003 Chin. J. Appl. Ecol. 14 2044 (in Chinese) [张彦东, 白尚斌 2003 应用生态学报 14 2044]
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[1] Bai C Y, Yan Y, Mei D C 2010 Chin. Phys. B 19 060503
[2] Zheng Z R, Su W H, Su Y 2007 Acta Phys. Sin. 56 6989 (in Chinese) [郑植仁, 苏文辉, 苏艳 2007 56 6989]
[3] Zhang L, Cao L 2011 Commun. Theor. Phys. 55 462
[4] Wang C J, Wei Q, Mei D C. 2007 Modern Phys. Lett. B 21 789
[5] Yu A H 2003 M. S. Dissertation (Nanjing: Nanjing Forestry University) (in Chinese) [余爱华 2003 硕士学位论文 (南京: 南京林业大学)]
[6] Fang C J 2012 J. Hubei Univ. Technol. 27 92 (in Chinese) [方次军 2012 湖北工业大学学报 27 92]
[7] Bie M J, Zhong W R, Chen H D, Li L, Shao Y Z 2009 Acta Phys. Sin. 58 97 (in Chinese) [别梦杰, 钟伟荣, 陈虎弟, 李立, 邵元智 2009 58 97]
[8] Yang J H, Liu X B 2010 Acta Phys. Sin. 59 3727 (in Chinese) [杨建华, 刘先斌 2010 59 3727]
[9] Liu Z H, Zhou Y R, Zhang A Y, Pang X F 2010 Acta Phys. Sin. 59 699 (in Chinese) [刘志宏, 周玉荣, 张安英, 庞小峰 2010 59 699]
[10] Guo Y F, Xu W 2008 Acta Phys. Sin. 57 6081 (in Chinese) [郭永峰, 徐伟 2008 57 6081]
[11] Zhang H Q, Lu L L, Yan X L, Gao P J 2007 Sci. China 37 246 (in Chinese) [张怀强, 卢丽丽, 阎雪岚, 高培基 2007 中国科学 37 246]
[12] Meng X Y 2006 Forest Mensuration (3nd Ed.) (Beijing: China Forestry Publishing House) pp179–201 (in Chinese) [孟宪宇 2006 测树学(第三版)(北京: 中国林业出版社)第179–201页]
[13] Xing F, Yao S K, Li M L 2011 J. Capital Normal Univ. 32 1 (in Chinese) [邢菲, 姚少魁, 李民丽 2011 首都师范大学学报 32 1]
[14] Chen J, Cheng C M 2008 J. Huazhong Normal Univ. 42 207 (in Chinese) [陈俊, 成传明 2008 华中师范大学学报 42 207]
[15] Han L B 2008 Acta Phys. Sin. 2008 57 2699 (in Chinese) [韩立波 2008 57 2699]
[16] Jia Y, Li J R 1996 Phys. Rev. E 53 5786
[17] Wu D J, Cao L, Ke S Z 1994 Phys. Rev. E 50 2496
[18] Kubo R 1963 J. Math. Phys. 4 174
[19] Novikov E A 1919 Zh. Eksp. Teor. Fiz. 20 1290
[20] Peter J, Peter H 1987 Phys. Rev. A 35 4464
[21] Hu G 1994 Stochastic Forces and Nonlinear System (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) [胡岗 1994 随机力与非线性系统(上海: 上海科技教育出版社)]
[22] Wang C J, Wei Q, Zheng B B, Mei D C 2008 Acta Phys. Sin. 57 1375 (in Chinese) [王参军, 魏群, 郑宝兵, 梅冬成 2008 57 1375]
[23] Nie L R, Mei D C 2007 Phys. Lett. A 371 111
[24] Zhang Y D, Bai S B 2003 Chin. J. Appl. Ecol. 14 2044 (in Chinese) [张彦东, 白尚斌 2003 应用生态学报 14 2044]
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