The fourth fundamental circuit element, the memristor, has become a promising candidate to substantially improve the energy and area efficiencies of circuits as traditional complementary metal-oxide-semiconductor (CMOS) technology is approaching its physical limit. However, a mathematical representation of the experimentally obtained current-voltage characteristic of the memristor is necessary to develop and test memristor-based circuitry in electrical design simulators. Here we have developed a behavioral model for the I-V trace of a Pt/TiO2/Pt memristor that can relate the fitting equations with the physical processes associated with the device in response to applied electrical excitation. Multiple conduction mechanisms are involved in memristor that depend upon its latest state. Therefore, the I-V has distinct segments that altogether form a hysteresis loop pinched at the center. In accordance with the predominant conduction mechanisms at each segment, our model defines the form of the equations. The behavioral model can adequately represent the experimental I-V retrieved from existing work.

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