Maxwell demon in Granular gas: a new kind of bifurcation? The hypercritical bifurcation

19 pages, 10 figuresThis paper starts with the investigation of the behaviour of a set of two subsystems which are able to exchange some internal quantity according to a given flux function. It is found that this sytem exhibit a bifurcation when the flux passes through a maximum and that its kind (super-critical/sub-critical) depends on the dissymmetry of the flux function near the maximum. It is also found a new kind of bifurcation when the flux function is symmetric: we call it hypercritical bifurcation because it generates much stronger fluctuations than the super-critical one. The effect of a white noise is then investigated. We show that an experimental set-up, leading to the Maxwell demon in granular gas, displays all these kinds of bifurcation, just by changing the parameters of excitation. It means that this system is much less simple as it was thought