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An iterative map for the buck-boost converter under current-mode control is developed as a basis for the chaos and bifurcation study. This discrete model is used to examine the bifurcation phenomena under variations of input voltage, reference current and load resistance. With the help of the loci of eigenvalues of a Jacobian matrix, the first bifurcation point of the buck-boost converter is investigated in detail. The theoretical analysis agrees with the numerical simulation. A frequency-scaling theorem and boundary-condition observation are also presented that are useful for the prediction of the first flip bifurcation.