Nonlinear Dynamical Systems

Nonlinear dynamical systems are systems where changes in the state of the system do not happen in a straight-line manner. Instead, small changes in initial conditions can lead to vastly different outcomes, often referred to as the "butterfly effect." These systems are common in nature, such as weather patterns or ecosystems, where interactions are complex and interconnected. Unlike linear systems, where responses are predictable and proportional to inputs, nonlinear systems can exhibit unpredictable behaviors, including chaos, making them challenging to analyze and understand.