On the Composition of Describing Functions in Feedback Loops

A first model developed by the authors for the study of pathological oscillations in Parkinson's disease is reviewed. This provides conditions for onset and extinction of almost sinusoidal oscillations. The describing function approach for use in such a situation is introduced and it is shown that the two describing functions used here may be “composed” into a single equivalent describing function. Conditions at onset or quenching of oscillation are noted, but wider applications have yet to be developed.