Linear and nonlinear systems

Linear systems are mathematical models where the output is directly proportional to the input, meaning if you double the input, the output also doubles. They follow the principle of superposition, allowing for straightforward predictions. Nonlinear systems, on the other hand, involve relationships where the output doesn't change proportionally with the input, often resulting in complex behaviors like chaos or multiple outcomes. These systems are more challenging to analyze and predict because small changes in input can lead to vastly different results. Understanding whether a system is linear or nonlinear helps in choosing the right methods to study and solve it.