色关联噪声对林木Logistic生长模型的影响

王国威; 徐大海; 程庆华

doi:10.7498/aps.62.224208

长江大学物理科学与技术学院,荆州,434023

Influences of correlated colored-noises on logistic model for tree growth

摘要: 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λ<0时，随着|λ|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。

关键词:

Abstract: 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 ofλ>0, the position of peak moves toward right as D increases, but it is opposite for the case ofλ<0 as Q increases.

色关联噪声对林木Logistic生长模型的影响

长江大学物理科学与技术学院,荆州,434023

关键词:

Influences of correlated colored-noises on logistic model for tree growth

长江大学物理科学与技术学院,荆州,434023

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