First, reset the parameters to their default values by quitting and restarting the applet. Now set, for example, dX0=0.004, i.e. prepare two initial conditions that differ by one part in a thousand.
Start the evolution, plotting Z(t) against X(t) (i.e. set x-ax=1 and y-ax=3).
Initially the two solutions track each other so closely that only one orbit appears on the screen. By a time as short as t=10 the difference has grown large enough to be visible, and by time t=15 the trajectories no longer track each other at all. The behavior is particularly apparent in a direct X(t) plot (set x-ax=0). In only 15 characteristic time units for the dynamics, we have completely lost the ability to forecast the behavior if the "error" in our initial conditions is only one part in a thousand!
Study the existence of the butterfly effect for different values of a.