Would be quite a challenge to come up with a system that has all eight styles. But as far as generating each one separately, do you know about the Trace-Determinant? If not, look it up. Now draw a circle around the origin in the T-D coordinate system. As the point (t,d) moves over this circle, it will pass through regions corresponding to each of the dynamic types. Now, calculate the coefficients corresponding to (t,d) for each region for the system:
and the phase-space diagram for that system will pass through all eight of the dynamic styles as the point (t,d) travels around the circle.