Dynamics of quantitative homeostasis: VIII. Processes that oscillate finitely many times

There is no well-established method of dealing with medical processes that oscillate only a finite number of times. A lagged homeostatic model of higher power in certain circumstances follows such a pattern and critical values are here explored by numerical integration. Abrupt ending of the oscillation occurs with processes of higher powers. The model is illustrated by clonus, chosen because reflexes are naturally lagged responses and because clonus may be unsustained. In applying the model to clonus, there are some incongruities (notably inertia) that call for caution; however, published data suggest that they may not be important. These imperfections notwithstanding, the correspondence is remarkably good. The model dealt with here, being simple and economical, is a useful first step to genetics; and some empirically testable deductions from the model are listed.