Shift of a limit cycle in biology: From pathological to physiological homeostasia*

Biological systems may show homeostatic behaviors that are similar to the ones of forced dynamic systems with a stable limit cycle. For a large class of dynamic systems, it is shown that a shift of a pathological limit cycle over the physiological limit cycle can never be executed by means of a control with a desired periodicity. The above statement shows that the only possibility is to reduce as much as possible the dimensions of a small residual limit cycle. Moreover, it is possible to give some information about the structure of feedback laws that would allow the shift of the limit cycle. The fact that it is generally not possible to recover a physiological limit cycle from a pathological one, results into the fear of never or hardly ever reaching a physiological behavior, and it seems that any hope of therapeutics is given up. This leads to introduce the locking concept, which permits system parameters to change and provides the basis for an adaptive and iterative control, which allows a step by step approach and to finally reach the physiological limit cycle. (c) 1995 American Institute of Physics.