  We model the photometry of RS CVn star $\sigma$ Geminorum to obtain new
information on the changes of the surface starspot distribution, i.e., activity
cycles, differential rotation and active longitudes. We use the previously
published Continuous Periods Search-method (CPS) to analyse V-band differential
photometry obtained between the years 1987 and 2010 with the T3 0.4 m Automated
Telescope at the Fairborn Observatory. The CPS-method divides data into short
subsets and then models the light curves with Fourier-models of variable orders
and provides estimates of the mean magnitude, amplitude, period and light curve
minima. These light curve parameters are then analysed for signs of activity
cycles, differential rotation and active longitudes. We confirm the presence of
two previously found stable active longitudes, synchronised with the orbital
period $P_{\rm{orb}}=19.60$d and find eight events where the active longitudes
are disrupted. The epochs of the primary light curve minima rotate with a
shorter period $P_{\rm{min,1}}=19.47$d than the orbital motion. If the
variations in the photometric rotation period were to be caused by differential
rotation, this would give a differential rotation coefficient of $\alpha \ge
0.103$. The presence of two slightly different periods of active regions may
indicate a superposition of two dynamo modes, one stationary in the orbital
frame and the other one propagating in the azimuthal direction. Our estimate of
the differential rotation is much higher than previous results. However,
simulations show that this can be caused by insufficient sampling in our data.
