Nonlinear systems are mathematical models where the output is not directly proportional to the input. This means that small changes in the input can lead to large and unpredictable changes in the output. Nonlinear systems are common in various fields, including physics, biology, and economics, where complex interactions occur. Examples of nonlinear systems include weather patterns, population dynamics, and electrical circuits. Unlike linear systems, which can be easily analyzed and predicted, nonlinear systems often require advanced techniques for understanding their behavior. This complexity can lead to phenomena such as chaos, where small differences in initial conditions result in vastly different outcomes.