FRACTAL GEOMETRY-BASED NONLINEAR MODELING OF ECONOMIC SYSTEMS

Abstract

This article presents a deep mathematical and analytical investigation into the application of fractal geometry in the nonlinear modeling of complex economic systems. By synthesizing concepts from chaos theory, dynamic systems, and fractal mathematics, the study demonstrates how economic indicators such as price volatility, investment behavior, and financial risk display fractal characteristics over multiple scales. The research develops a comprehensive fractal model based on Hausdorff dimension and Lyapunov exponents to capture irregular yet patterned dynamics of economic systems. Using time-series data and simulated trajectories, the model identifies critical thresholds of instability and self-organization, revealing that economic behavior evolves through deterministic chaos rather than random fluctuations. The findings contribute to modern econophysics and provide quantitative tools for long-term forecasting, sustainability assessment, and systemic-risk management in financial markets.