The memristor is an electrical circuit element that is similar to a resistor but has the potential to maintain state between turning power on and off. These memristors are about half the size of the transistors found in current flash storage technology, allowing capacity of these devices to double. This paper discusses the basics of memristors, which is an electrical circuit element, and presents the first principle simulation results of Pt/TiO 2-x - TiO 2/Pt system where the central region has a boundary separating TiO 2-x and TiO 2 regions. This barrier is progressively shifted towards the TiO 2-x region with applied bias to gradually increase the thickness of TiO 2 region. A comparison of the electrical characteristics of the device when the TiO 2 region is extended towards TiO 2-x region is also presented. The basis of memristive behavior, the non linear hysteresis curve of memristor, has been obtained based upon the simulation results. © 2012 IEEE.