Taking total ampere-turns of the primary and secondary windings of the transformer as one of state variables, the discrete time model of current controlled flyback converter with two borderlines of total ampere-turns is established, and the corresponding stabilities are analyzed by utilizing Jacobian to calculate the eigenvalues. Furthermore, by using the bifurcation diagrams and the maximal Lyapunov exponent spectrums, bifurcation analyses and operation state estimations of the flyback converter are performed. The results by PSIM circuit simulations verify the validity of the theoretical analysis and indicate that when the parameters vary, there exist complex nonlinear phenomena, such as period-doubling bifurcation, border collision bifurcation, chaos, period-window, etc., and there are three different operation states of periodic state, CCM robust chaotic state and DCM weak chaotic state in current controlled flyback converter.