Chaotic Behavior in the Double Well Oscillator

Here we see the system running with a large forcing amplitude, the entire parameter set for this behavior is
 

initial position = 1.0
initial velocity = 0.0
forcing amplitude = 0.4
forcing frequency = 1.0
dampening constant = 0.25


For these values, the system seems to have lost all of its nice periodic behavior. However, the motion is still bounded in the phase space. This is a new kind of behavior. It does not diverge to infinity as the time goes to infinity, but it also never repeats itself. This behavior is chaotic behavior, the trajectory will bounce around the phase space, never repeating itself. The time and velocity plots for these settings look like this.