A dynamical system is a mathematical model used to describe how a point in a given space evolves over time according to a set of rules. These systems can be continuous, where changes occur smoothly, or discrete, where changes happen at specific intervals. They are often represented using equations that capture the relationships between variables. Dynamical systems are widely applied in various fields, including physics, biology, and economics. For example, they can model the behavior of pendulums, the spread of diseases, or the fluctuations in financial markets. Understanding these systems helps predict future behavior based on current conditions.