FIGURE 2. The coupled variable-resistor model for a memristor.

a, Diagram with a simplified equivalent circuit. V, voltmeter; A, ammeter. b, c, The applied voltage (blue) and resulting current (green) as a function of time t for a typical memristor. In b the applied voltage is v₀sin(₀t) and the resistance ratio is , and in c the applied voltage is v₀sin²(₀t) and , where v₀ is the magnitude of the applied voltage and ₀ is the frequency. The numbers 1–6 label successive waves in the applied voltage and the corresponding loops in the i–v curves. In each plot the axes are dimensionless, with voltage, current, time, flux and charge expressed in units of v₀ = 1 V, , t₀  2/₀  D²/_Vv₀ = 10 ms, v₀t₀ and i₀t₀, respectively. Here i₀ denotes the maximum possible current through the device, and t₀ is the shortest time required for linear drift of dopants across the full device length in a uniform field v₀/D, for example with D = 10 nm and _V = 10^-10 cm² s^-1 V^-1. We note that, for the parameters chosen, the applied bias never forces either of the two resistive regions to collapse; for example, w/D does not approach zero or one (shown with dashed lines in the middle plots in b and c). Also, the dashed i–v plot in b demonstrates the hysteresis collapse observed with a tenfold increase in sweep frequency. The insets in the i–v plots in b and c show that for these examples the charge is a single-valued function of the flux, as it must be in a memristor.