Many nanostructures exhibit electrically stimulated change of resistance and have been proposed as the basis for non-volatile random access memories (NVRAM), but progress toward implementation has been delayed by difﬁculties in understanding and controlling the resistive switching phenomena . To design a device that can be reliably used for information processing, one needs (i) a mathematically consistent theory for modeling the circuit component, and (ii) knowledge of the underlying operating principles so that one might improve a device by ﬁne tuning parameters such as doping and geometrical proﬁle. Recent breakthrough occurred at Hewlett-Packard Laboratories has been receiving increasing attention in both fundamental researches and commercial applications. In May 2008, HP scientists announced the discovery of the missing circuit element memristor, acronym for memory resistor. The memristor concept gives a simple explanation for many puzzling voltage-current characteristics in nanoscale electronics . Researchers also clariﬁed coupled electron-ion dynamics responsible for memristive switch . With the reported advance, HP is promising prototypes of ultradense memory chips in 2009.