Dynamical Systems Theory is a mathematical framework used to study how systems evolve over time. It focuses on understanding the behavior of complex systems, which can be described by differential equations or discrete maps. This theory helps analyze stability, chaos, and periodicity in various fields, including physics, biology, and economics. In this context, a dynamical system consists of a set of variables and rules that dictate their interactions. By examining these systems, researchers can predict future states and understand underlying patterns, making it a valuable tool in both theoretical and applied sciences.