A dynamical system is a mathematical framework used to describe 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 often represented by equations that capture the relationships between variables. Dynamical systems are widely applied in various fields, including physics, biology, and economics. For example, the behavior of populations in ecology can be modeled using dynamical systems, helping researchers understand growth patterns and interactions. Other applications include studying the motion of planets in celestial mechanics and predicting market trends in finance.