Abstract: After dimension reduction, the I² controlled buck converter is studied and its one-dimensional discrete iterative map model is established in this paper. Based on the model, the nonlinear dynamic characteristics of the I² controlled buck converter is studied. Through the bifurcation analysis with the variations sensing resistance R_s and proportional coefficient k₁ of error amplifier, the operation states from the stable period-1 to the period-double bifurcation and from the robust chaos in continuous conduction mode (CCM) to the intermittent chaos in discontinuous conduction mode (DCM) are studied. Through analysis of R_s-V_o and k₁-V_o parameter spaces and discrete-time iterative mappings, the stability and operation mode transitions can be studied, the correctness of the theoretical analysis can be verified.