ABSTRACT
Trajectories in both the nonchaotic and chaotic regimes of nonlinear, dissipative systems have at least one thing in common: once we choose the control parameter, all trajectories (no matter what value we use for x0 to start iterating) go to an attractor. There's also an important difference in trajectories of the two regimes. For nonchaotic circumstances, trajectories for two different values of starting conditions (x0) get closer together (in most cases) or remain equidistant (on tori), for the same value of the control parameter. In the chaotic domain, however, it's just the opposite: trajectories diverge.
