Fuzzy-Initialized Logistic Dynamics for Macroeconomic Business Cycles: A Topological Framework

Abstract

We develop a mathematical framework connecting fuzzy logic inference with deterministic nonlinear dynamics for macroeconomic modeling. Starting from linguistic policy variables encoded via continuous fuzzy membership func- tions, we prove that the state space inherits a canonical compact metrizable topology. Using Takagi-Sugeno fuzzy inference, we construct a well-posed ordinary differential equation and establish topological conjugacy with multidi- mensional logistic dynamics. We characterize the stabil- ity properties of fixed points and prove existence, unique- ness, and continuous dependence of solutions. The frame- work enables analytical treatment of qualitative economic communications within dynamical systems theory, with applications to inflation forecasting and policy design.