First, various limit cycles in particle physics are searched. Next, we investigate the relations among the limit cycle and the oscillation-wave, and the limit cycles in the gauge field and the dynamical model, and the gauge field and the qualitative analysis theory, etc. Further, we research the limit cycle and some unified theories on particle. The limit cycle is also a special string. Some new mathematical results and equations are obtained. Finally, various possible developments of the limit cycle are proposed.