A Study of Global Dynamics and Oscillatory Behavior of Rational-Type Nonlinear Fuzzy Difference Equations with Exponential Decay

The concept of fuzzy modeling and fuzzy system design has opened new horizons of research in functional analysis, having a significant impact on major fields such as data science, machine learning, and so on. In this research, we use fuzzy set theory to analyze the global dynamics and oscillatory behavior of nonlinear fuzzy difference equations with exponential decay. We discuss the stability, oscillatory patterns, and convergence of solutions under different initial conditions. The exponential structure simplifies the analysis while providing a clear understanding of the system’s behavior over time. The study reveals how fuzzy parameters influence growth or decay trends, emphasizing the method’s effectiveness in handling uncertainty. Our findings advance the understanding of higher-order fuzzy difference equations and their potential applications in modeling systems with imprecise data. Using the characterization theorem, we convert a fuzzy difference equation into two crisp difference equations. The g-division technique was used to investigate local and global stability and boundedness in dynamics. We validate our theoretical results using numerical simulations.