  We investigate the nature of the parallel-roll to spiral-defect-chaos (SDC)
transition in Rayleigh-Benard convection, based on the generalized
Swift-Hohenberg model. We carry out extensive, systematic numerical studies by,
on one branch, increasing the control parameter gradually from the parallel
roll regime to the SDC regime and, on the other branch, decreasing it in the
opposite manner. We find that the data of several time-averaged global
quantities all form hysteretic loops from the two branches. We also discuss
several possible scenarios for the transition and analyze our data for SDC
accordingly. We conclude that the roll-to-SDC transition is first-order in
character and that the correlation length diverges at the conduction to
convection onset. We further postulate that this transition can be understood
somewhat similar to the hexagon-to-roll transition in non-Boussinesq fluids.
Finally we comment on the differences between our conclusion and those in two
experiments.
