Transient Chaos in the Double Well Oscillator

The settings for the behavior shown below are :

initial position = 1.0
initial velocity = 0.0
forcing amplitude = 0.245
forcing frequency = 1.0
dampening constant = 0.25

Now the system seems to have lost it's order, at least it seems so at first. The cycle that the system falls into 
is stable, but the trajectory seems at first to be caught in chaotic behavior. 

To get this behavior, only the forcing term was changed from the last section.

In the following position and velocity plots, the chaotic behavior near the beginning of the trajectory can easily be seen, and the steady state behavior is easy to pick out as well.

Position vs. Time Plot

Velocity vs. Time Plot

Still this behavior is not especially interesting. The system settles down into a periodic solution similar to the solutions of many linear problems. So, lets give the forcing amplitude another increase, and see what happens.