Dynamical Systems and Differential Equations

Dynamical systems study how things change over time, often using mathematical equations to model this behavior. Differential equations, a key tool in this field, describe relationships involving rates of change, like how speed varies with distance. In essence, they help us understand complex systems, such as population growth or the motion of planets, by capturing how one state evolves into another. By analyzing these equations, we can predict future behavior and identify patterns, making them essential in fields such as physics, biology, and economics.