This comunication is based on a preliminary work which emphasized a topological model of biomembranes from Thom's Catastrophe Theory. In this model called swallowtail bifurcation set, the structural state of a biomembrane was within the control of two structural attractors. Then, the physiological act of this biomembrane resulted in a sudden transfer of weight from the hydrophilic attractor to the hydrophobic attractor.In this consecutive work, the physiological act appears to be one of the four stages which permit to describe the (...) larger notion of cyclic membrane function. Two of these stages unfold in the structural axis of the swallowtail model. They prepare the two others (physiological act and refractory stages) which expand in the functional direction. (shrink)