  We propose a simple model of a nanoswitch as a memory resistor. The
resistance of the nanoswitch is determined by electron tunneling through a
nanoparticle diffusing around one or more potential minima located between the
electrodes in the presence of Joule's heat dissipation. In the case of a single
potential minimum, we observe hysteresis of the resistance at finite applied
currents and a negative differential resistance. For two (or more) minima the
switching mechanism is non-volatile, meaning that the memristor can switch to a
resistive state of choice and stay there. Moreover, the noise spectra of the
switch exhibit $1/f^2\rightarrow 1/f$ crossover, in agreement with recent
experimental results.
