The dynamics of quantifiable homeostasis. IV: Zero-order homeostasis

A zero-order homeostatic process is one in which the corrective force a has sign opposite to that of what the displacement from the homing value was one lag (L) time earlier, but is unrelated to magnitude of displacement. The properties of a zero-order process are considered in some detail. Its stable state is an oscillation with a period of 4L and a maximum amplitude of aL. It is suggested that this property is exploited in evolution for intrinsically rhythmical processes, and several examples (respiration, menstruation, and heart beat) are discussed. The parameters may be modulated by an ancillary cybernetic (retreat) circuit and hence the properties of the oscillation controlled as need be. Zero-order oscillation has means of conserving information through phase shifts. Also, when it is combined with a linear cybernetic process (with restoration constant b), it prevents information in the latter from dying out, even if Lb is less than pi/2 (which in a pure linear process would ensure extinction of all signs of perturbation). A further elaboration is the Dilman process of zero order in which there is a threshold of displacement below which homeostatic responses are not evoked. The merits of the value of the threshold are discussed. The properties of the zero-order process with a first-order retreat function furnish a tentative explanation for why hormonal homeostasis does not operate directly through the pituitary but involves the hypothalamus and intermediate hormone-releasing factors.