Constructing non-fixed-point maps with memristors

Chaotic maps, memristive maps, and maps with special fixed points have attracted significant researches recently. We introduce a simple methodology to construct a memristor-based map without fixed points in this work. In our methodology, a tiny perturbation is included into a memristor-based map to change its fixed points. Therefore, the presence and disappearance of fixed points can be controlled. By considering two general structures of discrete maps, seven memristive non-fixed-point maps have been reported. We have found that the methodology is useful for designing not only non-fixed-point maps with memristor but also non-fixed-point maps without memristor. To confirm the physical realization of the proposed maps, a hardware implementation of one of such maps is performed using a microcontroller.