Exploring Nonlinear Dynamics in High-Dimensional Systems: Applications to Chaos Theory and Fractal Geometry

Abstract

The phenomena in math, physics, biology, and economics are based on nonlinear dynamics in highdimensional systems. This review examines the principles of nonlinear dynamics, and how it is applied to the chaos theory and fractal geometry. Bifurcation, strange attractors, and fractal sets are some of the important ideas that we talk about and explain how high-dimensional systems display unpredictable and complicated behavior. The paper also explores the modeling of these phenomena, mathematical tools to study them and their applicability in practical situations. This review brings together the recent developments, thus indicating the point of convergence between chaos and fractals and their application to the study of complex systems.