Academic Journal of Mathematical Sciences, 2025, 6(2); doi: 10.25236/AJMS.2025.060205.
Fu Yan1, Pan Xilin1, Xie Shu1, Zheng Yihan1, Peng Yuxin1, Yang Yi1, Wang Guowei2
1School of Mathematics and Computer Science, Yuzhang Normal University, Nanchang, China
2School of Education, Nanchang Institute of Science and Technology, Nanchang, China
A non-deterministic Langevin equation is obtained by introducing multiplicative and additive Gaussian white noise in the Logistic model of tree growth, and an approximate Fokker-Planck equation is derived through calculations by using the Liouville equation, Novikov’s theorem, and nonlinear approximation. The equation is solved under steady-state conditions, and the impact of noise-related parameters on the steady-state probability distribution function is systematically discussed. Obtained results show that changing the multiplicative white noise intensity D and additive white noise intensity Q can lead to the change of peak height and peak position of steady-state probability distribution curve, and have a drift effect on the probability density distribution. However, the change of the value of the steady-state probability distribution curve and the direction of the peak position are different in the process of increasing D and Q. The height of the peak becomes higher as multiplicative noise intensity D increases, but the width of the peak becomes narrower and the position of the peak shifts to the left. When additive noise intensity Q increases, the peak height decreases, but the width of the peak increases and the position of the peak shifts to the right. In addition, when noise correlation strength λ>0, it is found that there are no two peaks in the image, which does not conform to the regularity of tree growth, so we only discuss the case of noise correlation strength λ<0. With the increase of noise correlation strength λ, the peak height of steady-state probability distribution function shows a decreasing trend, accompanied by the phenomenon of increasing peak width and right shift of peak position.
Trees Grow Model; Logistic Model; White Noise; Steady-State Probability Distribution
Fu Yan, Pan Xilin, Xie Shu, Zheng Yihan, Peng Yuxin, Yang Yi, Wang Guowei. Steady-State Properties of Forest Growth Model under the Influence of Correlation Noise. Academic Journal of Mathematical Sciences (2025), Vol. 6, Issue 2: 33-40. https://doi.org/10.25236/AJMS.2025.060205.
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