Interactions between centrally and peripherally generated neuromuscular oscillations

An experimentally based model of the mammalian neuromuscular system has been extended to include the interaction of sinusoidal inputs generated within the central nervous system and those produced peripherally by reflex pathways, together with muscle properties and external loads. Multiple reflex pathways and pathways having acceleration as well as velocity and length sensitivity and considered. The responses are analyzed for brief inputs (Dirac delta-functions), sinusoidal driving functions and mixtures of the two over ranges in which the model behaves either linearly or non-linearly. Approximate solutions are derived for the non-linear range, and exact numerical solutions are computed for a few examples within the linear range. The extent to which brief inputs can reset ongoing oscillations and the extent to which sinusoidal inputs can entrain these oscillations are of particular interest.