What does "nonlinear dynamics" study?

Nonlinear dynamics studies systems governed by nonlinear equations, which often exhibit complex behaviors that can be highly sensitive to initial conditions. In such systems, small changes in initial parameters can lead to vastly different behaviors, a phenomenon commonly referred to as chaos. This area of study encompasses a broad range of applications, from understanding the motion of double pendulums to predicting weather patterns and analyzing ecological models.

The nature of nonlinear systems allows for phenomena such as bifurcations, where a small change in the parameter values of the system results in a sudden qualitative change in its behavior, and limit cycles, where certain behaviors can lead to periodic motion. In contrast to linear systems, which typically produce predictable and proportional responses to inputs, nonlinear dynamics involves complexities and unpredictabilities that require specialized analytical and numerical methods for their study.

The other options pertain to linear dynamics, static equilibrium states, or simple harmonic motions, all of which do not capture the essence and breadth of nonlinear dynamics. Thus, the focus on complex behaviors in systems governed by nonlinear equations makes the first option the most accurate representation of what nonlinear dynamics investigates.