The model of high speed train pantograph-catenary system is established and analyzed using the perturbation method, the stable regions and periodic solution of the dynamics system are obtained, the Lyapunov exponents of the pantograph-catenary system are calculated, results show that the conclusions are same for analyzing the stable current-collecting of catenary-pantograph system with the two kind methods , which would be very useful for studying the high speed catenary-pantograph system and designing the new type pantograph .