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This paper studies a frequency bifurcation phenomenon of a soft-switched push-pull contactless power transfer (CPT) system with parallel tuned pick-up and short-circuit decoupling power flow control. An extended stroboscopic mapping method is applied to obtain the possible zero voltage switching (ZVS) operating points first, then the fundamental resonant operating points are defined, and the system soft switching stability is analyzed according to the eigenvalues of the Jacobi matrix of the Poincare mapping model of the system. An example system with multiple resonant frequency points is studied and verified by simulation results. Frequency hopping phenomenon is identified and discussed in the system when the switch of the decoupling power flow controller is turned on and off with a very low frequency. The results are very useful for guiding the design of practical CPT systems, and the proposed method can also be applied to analyze nonlinear behaviors in other switch-mode resonant converters.