Order in chaos

Today I was reading on oscillators and chaos, trying to find supporting material for my oscillator model of neural nets. On the way I ran into a java applet, the Phase plane plotter. When you enter for example the equations:
x' = x - y*0.1231+cos(x*y*x)
y' = x + y*x*sin(x+y)

Then set the window boundries to (-100,-100) x (100,100)
and click in the plane window randomly a few hundred times. You will see that most lines get into one certain area, you can see a pattern in the distribution of the chaos. Although the whole plane is probably convered, there is an area shaped by the nature of the equations in which the systems is more likely to reside. It reminds me of the distribution pattern of an electron around a proton. Let's see what more reading brings...