Abstract: By Studying and calculating poincare section. power spectrum and Lyapunov exponents about the system of J-J type, we have obtained:(1)When some parameters vary and the rotating number is fixed, there is the route of quasi-period to chaos, which embodies that the fixed circle produces kinks at first, and with Jerking-lengthening and compression of kinks, then develops into station of chaos.(2) There is only outer-kinks in the single system of J-J type, and there are two kinks, inter-kinks and outer-kinks in the double system of J-J type.

Key words: staircase, kinks, chaos, rotating number