Higher-Order Fuzzy Difference Equations: Existence, Stability, and Illustrative Numerical Examples

This paper examines the dynamics of positive solutions to a system of fuzzy difference equations, which provide effective tools for modeling dynamical systems with uncertain or imprecise parameters. The main objective is to establish the existence, uniqueness, and qualitative properties of positive solutions within a fuzzy framework. After recalling some fundamental notions from fuzzy set theory, we analyze the dynamics of the proposed system. The main results prove the existence of a unique positive fuzzy solution under suitable conditions and establish the boundedness, continuity, and convergence of the solutions. In particular, all solutions converge to a unique positive equilibrium point. Numerical experiments for (l1,l2)=(2,3) and (l1,l2)=(4,1) with uncertainty levels γ=0.2 and γ=0.8 illustrate the theoretical results and confirm the convergence toward the unique positive equilibrium.