Coupled rate equaiton for passive or self Q switched solid state lasers is studied in physics and mathematics methods.The formula about relationship to repetition rate of the pulses and optical parameters of the lasers has been derived,by means of the adiabatic elimination approximation (AEA) and the Hopf bifurcation condition.For the type of Cr:N d:YAG saturable absorber Q switched lasers,the theoretical calculations are agreement with the experimental results.