The bifurcation diagram for a vibro-fluidized granular gas in N connected
compartments is constructed and discussed. At vigorous driving, the uniform
distribution (in which the gas is equi-partitioned over the compartments) is
stable. But when the driving intensity is decreased this uniform distribution
becomes unstable and gives way to a clustered state. For the simplest case,
N=2, this transition takes place via a pitchfork bifurcation but for all N>2
the transition involves saddle-node bifurcations. The associated hysteresis
becomes more and more pronounced for growing N. In the bifurcation diagram,
apart from the uniform and the one-peaked distributions, also a number of
multi-peaked solutions occur. These are transient states. Their physical
relevance is discussed in the context of a stability analysis.Comment: Phys. Rev. E, in press. Figure quality has been reduced in order to
decrease file-siz
