We present a novel kind of integrate-and-fire circuit (IFC) with two periodic inputs: a pulse-train stimulation input and a base input. We clarify that the system state is quantized by the pulse-train stimulation input. Then the system dynamics is described by a return map with quantized state (Qmap). By changing the shape of the base input, various Qmaps can be obtained. The Qmap exhibits co-existence state of various super-stable periodic orbits, and the IFC outputs one of corresponding super-stable periodic pulse-trains depending on the initial state. For a typical case, we clarify the number of co-existing periodic pulse-trains theoretically for the stimulation frequencies. Constructing a simple test circuit, typical phenomena can be verified in the laboratory.