Imagine that at each time step you magically connect the X component of two systems of Lorenz equations, meaning that the value of X used in the equation for attractor 1 is copied over to attractor 2. Then you compute the X,Y and Z at t+1 for both attractors as usual.
<p>In the above applet you see this effect. The continuous line is attractor 1 (the reference) and the dashed lines are from the attractor 2 (the coupled attractor), meaning that at each time step the X value from 1 is copied over to 2.</p> <p>The white line measures the distance between two trajectories as time passes. In this case we can quickly see it dropping down to zero and synchronization occurs.</p> <p>This changes the behaviour of the system completely. Instead of being two systems with divergent trajectories they get closer and closer until finally they overlap perfectly, travelling in sync through space.</p>
more details at the Lorenz Sync Page (with extra applets)