  We present a numerical model which allows us to study the Kelvin force probe
microscopy response to the charge switching in quantum dots at various time
scales. The model provides more insight into the behavior of frequency shift
and dissipated energy under different scanning conditions measuring a
temporarily charged quantum dot on surface. Namely, we analyze the dependence
of the frequency shift, its fluctuation and of the dissipated energy, on the
resonance frequency of tip and electron tunneling rates between tip - quantum
dot and quantum dot - sample. We discuss two complementary approaches to
simulating the charge dynamics, a stochastic and a deterministic one. In
addition, we derive analytic formulas valid for small amplitudes, describing
relations between the frequency shift, dissipated energy, and the
characteristic rates driving the charging and discharging processes.
