One of the rather familiar electronic devices that exhibit properties similar to those of a memristor (dependence of resistance on current at previous moments of time) is a **gas-discharge lamp**. Resistance $R$ of such lamp is determined by the concentration of free electrons $n_e$, which changes with current flow: \[\begin{cases}R=\dfrac{F}{n_\mathrm e}\\ \dfrac{\mathrm dn_\mathrm e}{\mathrm dt}=-\beta n_\mathrm e+\alpha VI,\end{cases}\]Here $F$ is determined by the geometry of the tube (in the simplest model, conductivity is proportional to concentration), the $-\beta n_\mathrm e$ term is responsible for the neutralization of free electrons as the result of collisions, and the last tern $\alpha VI$ is responsible for the thermal emission of electrons.

The lamp is connected to a source with EMF $\mathcal E$ and internal resistance $r$.

Suppose now the lamp is supplied with an alternating voltage $V(t)=V_0\cos\omega t$. The internal resistance of the voltage source is still equal to $r$.

In fact, the electron concentration depends on time, and in a first approximation this dependence can be represented as:\[n_\mathrm e(t)=n_{ 0}+n_{1}\cos(2\omega t+\phi),\]where $n_1\ll n_{0}$.

A change in concentration results in a change in lamp resistance. We define its maximum relative change as:\[\delta\equiv\frac{R_\max-R_\min}{R_\mathrm{avg}}.\]