This paper investigates the dynamic behavior of a class of nonlinear fuzzy difference equations with compound exponential terms. By using g-division, Lyapunov stability analysis, algebraic inequalities, and mathematical induction, the existence and uniqueness of positive fuzzy solutions are proved. In addition, the boundedness and persistence of these solutions are established, along with the global asymptotic stability of the unique positive equilibrium. Finally, numerical simulations are performed to verify the theoretical results. These findings refine the analysis framework for fuzzy systems with compound nonlinear terms. They also have potential applications in biological population control, economic resource allocation, and engineering systems with uncertain parameters.

In this article, global asymptotic stability and trajectory structure of the following high-order nonlinear difference equation

$$z_{n+1}=\frac{z_{n-1}{z}_{n-2}{z}_{n-4}+z_{n-1}+z_{n-2}+z_{n-4}+b}{z_{n-1}{z}_{n-2}+z_{n-1}{z}_{n-4}+z_{n-2}{z}_{n-4}+1+b},n\in N,$$

are studied, where $b\in [0,\mathrm{\infty })$ and the initial conditions $z_i\in (0,\mathrm{\infty }),i=0,-1,-2,-3,-4.$ Using the semi-cycle analysis method, in a prime period, a continuous length of positive and negative semi-cycles of any nontrivial solution appears periodically: 2, 3, 4, 6, 12. Moreover, two examples are given to illustrate the effectiveness of theoretic analysis.