<p>This paper investigates the existence, boundedness, and long-term behavior of positive solutions in a system of fuzzy difference equations incorporating a third-order nonlinear term. The coefficients and initial conditions are assumed to be positive fuzzy numbers, forming a rigorous framework for analyzing the system’s qualitative dynamics. Theoretical results are complemented by numerical examples and a biologically inspired simulation that models the temporal interaction between a bacterial colony and antibiotic concentration under uncertainty. The graphical analysis illustrates key features such as uncertainty propagation and the effect of nonlinear parameters on system stability.</p>