This article examines the dynamic behavior of a second-order fuzzy difference equation that models the quantitative changes in a specific biological population: $$ E_{n+1}=\frac{S}{C+E_n+E_{n-1}},\ n\in \mathbb{Z}\ and\ n\ge 0,$$ Here, parameter $S$ represents the carrying capacity of the environment, while $C$ signifies the minimum resources required for population survival. The initial values $E_0$, $E_{-1}$, and parameters $S$ , $C$ are all positive fuzzy numbers. By employing the generalized division (g-division) with respect to fuzzy numbers, we establish the existence, uniqueness, persistence, and boundedness of positive fuzzy solutions to the equation under specified conditions. Furth... More >