色关联噪声对林木Logistic生长模型的影响

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： 林木生长 Logistic模型 色噪声 稳态概率分布

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

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 λ<0 as Q increases.
Keywords： tree growth Logistic model correlated noises steady-state probability distribution