The excitation-extintion line of hepatocytes from an inert state towards the stabilization of a given activity is described. Within the cell, the switching on of any given activity is a competitive process among different activities. The process is driven by the influence field created in the environment of the Rappaport acinus by sinusoidal blood which changes its characteristics during its passage from the portal zone to the central vein. Every step of the excitation-extintion pathway follows the so-called law of autoisodiasostasis (AIS), i.e. it is characterized by an oscillatory motion between restoring (homopoiesis or HP) and working (homeorhesis or HR) states. Since the cyclical bistable equilibrium of AIS characterizes all conditions of hepatocyte activities, the AIS cycle can be defined a limit cycle.