  It is now a widely held view that, in their formation and early evolution,
stars build up mass in bursts. The burst mode of star formation scenario
proposes that the stars grow in mass via episodic accretion of fragments
migrating from their gravitationally-unstable circumstellar discs and it
naturally explains the existence of observed pre-main-sequence bursts from high
mass protostars. We present a parameter study of hydrodynamical models of
massive young stellar objects (MYSOs) that explores the initial masses of the
collapsing clouds (Mc = 60-200Mo) and ratio of rotational-to-gravitational
energies (beta = 0:005-0:33). An increase in Mc and/or beta produces
protostellar accretion discs that are more prone to develop gravitational
instability and to experience bursts. We find that all MYSOs have bursts even
if their pre-stellar core is such that beta <= 0.01. Within our assumptions,
the lack of stable discs is therefore a major difference between low- and
high-mass star formation mechanisms. All our disc masses and disk-to-star mass
ratios Md=M* > 1 scale as a power-law with the stellar mass. Our results
confirm that massive protostars accrete about 40-60% of their mass in the burst
mode. The distribution of time periods between two consecutive bursts is
bimodal: there is a short duration (~ 1-10 yr) peak corresponding to the short,
faintest bursts and a long duration peak (at ~ 10^3-10^4 yr) corresponding to
the long, FU-Orionis-type bursts appearing in later disc evolution, i.e.,
around 30 kyr after disc formation. We discuss this bimodality in the context
of the structure of massive protostellar jets as potential signatures of
accretion burst history.
