The researchers studied how ship stern shaft-bearing systems behave when they rub against each other. They used a theory called attractor theory to analyze the system's dynamic responses. They found that when there is full rubbing, the system follows a circular pattern that gets bigger over time. When there is partial rubbing, the system goes from chaotic to organized motion, with the pattern changing in size. And when there is no rubbing, the system follows a circular pattern that gets smaller. These patterns show that the system can move in regular, semi-regular, or chaotic ways, depending on the rubbing.