Growth behaviors of dendritic sidebranches under random noises and characteristics of sidebranches modulated by external forces in directional solidification are studied by using phase field simulations. Simulation results show that, under random noises no regular sidebranches appears all the time, but sidebranches can be formed within a suitable range of frequencies. Moreover, strongly correlated sidebranches are formed at a fixed frequency and in a certain period, usually called a burst, to appear. There is no correlation between different bursts, but the frequency of every sidebranch within a burst is the same as its precursor, and this fixed frequency is consistent with the peak frequency of the whole spectrum of sidebranch. By introducing a time-periodic external force with a frequency in the range of the whole spectrum, regular dendritic sidebranches can be induced, and they can be most developed if the frequency of the external force is the same with that in a burst. The simulation results can provide guidance to control dendritic morphologies in solidification.