As i posted before these systems generate a metric based on the number of vertices including the star. That metric then generates a natural identity that the system converges back to in the face of any small disturbance.
It obviously looks like resonance but is integral to the whole system and is the natural stable solution available. All multi body systems will exhibit this characteristic.
Please reference my paper in Physics Essays (AIP) june 2010 to understand nth ordered metrics or nth ordered Pythagoreans.