A dynamical system is a mathematical model that describes how a point in a given space evolves over time according to specific rules. These systems can be continuous, where changes occur smoothly, or discrete, where changes happen at distinct intervals. They are used to study various phenomena in fields like physics, biology, and economics. In a dynamical system, the current state is determined by its previous states and the governing equations. Common examples include the motion of planets in space, population growth in ecology, and the behavior of chaotic systems. Understanding these systems helps predict future behavior and analyze stability.