A difference equation is a mathematical expression that relates the difference between successive values of a sequence. It is often used to model discrete systems, where changes occur at specific intervals, such as in economics or population studies. The equation typically involves terms that represent the current and previous values of the sequence, allowing for predictions about future values. Difference equations can be classified into two main types: linear and nonlinear. A linear difference equation has a constant relationship between terms, while a nonlinear one involves varying relationships. These equations are essential in fields like control theory and signal processing, where they help analyze and predict system behavior over time.