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Biped robots based on limit cycle walking paradigm commonly need less energy than other models and generate pretty natural gait, since this paradigm has fewer artificial constraints on walking motion compared to other conventional ones. To increase its performance and to realize a practical biped, the model needs further studies on its stability, disturbance rejection capability, and versatility, etc. In this paper, flat feet are added to increase its stability and disturbance rejection capabilities. Although flat feet model have been already studied, their stability properties are not clarified especially in the view of bifurcation route to chaos and global stability. The stability properties of modified feet models are analyzed and its effects are compared to the results of the simplest walking model whose stability properties are already well known.