title: Lyapunov function and the basin of attraction for a single-joint muscle-skeletal model.
abstract: This paper provides an explicit Lyapunov function for a general single-joint muscle-skeletal model. Using this Lyapunov function one can determine analytically large subsets of the basin of attraction of an asymptotically stable equilibrium. Besides providing an analytical tool for the analysis of such a system we consider an elbow model and show that the theoretical predictions are in agreement with experimental results. Moreover, we can thus distinguish between regions where the self-stabilizing properties of the muscle-skeletal system guarantee stability and regions where nerval control and reflexes are necessary.
authors.affiliation: Zentrum Mathematik, TU München, Boltzmannstr. 3, 85747 Garching bei München, Germany. giesl@ma.tum.de
authors.forename: Peter
authors.initials: P
authors.lastname: Giesl
authors.forename: Heiko
authors.initials: H
authors.lastname: Wagner
mesh_terms: D000818:Animals; D001696:Biomechanical Phenomena; D004551:Elbow Joint / Q000033:anatomy & histology / Q000502:physiology; D006801:Humans; D007596:Joints / Q000033:anatomy & histology / Q000502:physiology*; D008433:Mathematics; D008954:Models, Biological; D009119:Muscle Contraction; D009142:Musculoskeletal Physiological Phenomena; D009141:Musculoskeletal System / Q000033:anatomy & histology; D012018:Reflex / Q000502:physiology