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.
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