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

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 of λ >0, the position of peak moves toward right as D increases, but it is opposite for the case of λQ increases.