Steady-State Properties of Forest Growth Model under the Influence of Correlation Noise

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.