This is an interesting question. What you call a Darwin Solar System might refer to the theory of Charles Darwin's son, George Darwin, who was an expert in Cosmology and Mathematics. He and some other scientists like the French Laplace, proposed an idea for the formation of our Solar System, and this was long time ago.

George came up with the idea that four million years ago, the moon was pressed nearly against the earth and was rotating around it every 5 hours. Then he said that one day, a heavy tide occurred in the oceans which lifted it out, much as a ship is pushed out by winds from a bay, and floated out toward where it is now. George calculated the amount of time it would have taken for the movement of the ocean waves to give the Earth its current 24 hour day.

Because George Darwin was really interested in the planets and their origin, it is possible that the Darwin Solar System is just a way to name the work that he did in explaining the origin of our Solar System, according to the information that he had more than hundred years ago.

On the other hand, there is the Darwin's Space Mission which is trying to find information on the age of the Universe and the formation of our Solar System, and this is a NASA (National Aeronautics Space Administration) project.