  We study a sample of 21 young and active solar-type stars with spectral types
ranging from late F to mid K and characterize the behaviour of their activity.
We apply the continuous period search (CPS) time series analysis method on 16
to 27 years of photometry to estimate the surface differential rotation and
determine the existence and behaviour of active longitudes and activity cycles
on the stars. We supplement the time series results by calculating new
$\log{R'_{\rm HK}}$ emission indices for the stars from high resolution
spectroscopy. The photometric rotation period variations reveal a positive
correlation between the relative differential rotation coefficient and the
rotation period, but do not reveal any dependence of the differential rotation
on the effective temperature of the stars. Secondary period searches reveal
activity cycles in 18 of the stars and temporary or persistent active
longitudes in 11 of them. The activity cycles fall into specific activity
branches. We find a new split into sub-branches, indicating multiple
simultaneously present cycle modes. Active longitudes appear to be present only
on the more active stars. There is a sharp break at approximately $\log{R'_{\rm
HK}}=-4.46$ separating the less active stars with long-term axisymmetric spot
distributions from the more active ones with non-axisymmetric configurations.
In seven out of eleven of our stars with clearly detected long-term
non-axisymmetric spot activity the estimated active longitude periods are
significantly shorter than the mean photometric rotation periods. This
systematic trend can be interpreted either as a sign of the active longitudes
being sustained from a deeper level in the stellar interior than the individual
spots or as azimuthal dynamo waves exhibiting prograde propagation.
