title: An intrinsic mechanism for the oscillatory contraction of muscle.
abstract: A new model based on the theory of dynamical systems is proposed for the intrinsic random or systems is proposed for the intrinsic random or pseudo-random mechanism underlying certain types of muscular tremor. The active length-tension curve of the individual sarcomere, in conjunction with the passive length-tension relation is a map from length to tension with an observed time delay between length change and resulting tension change. The passive length tension relation is assumed to instantaneously relate this tension change back to a change in length. The stability properties of this iterated interval map are investigated by means of computer simulation and computation of the Lyapunov exponent and the bifurcation tree. The resulting analysis is related to experimental tremor data in the literature in terms of period doubling, bifurcation points, and "chaotic" behavior. The model appears to have its most fruitful application in understanding the insect type and isometric mammalian types of tremor.
mesh_terms: D000818:Animals; D001522:Behavior, Animal / Q000502:physiology; D001696:Biomechanical Phenomena; D008433:Mathematics; D008954:Models, Biological; D009119:Muscle Contraction; D009132:Muscles / Q000502:physiology*; D011898:Ranidae; D011930:Reaction Time / Q000502:physiology; D012518:Sarcomeres / Q000502:physiology; D013997:Time Factors