Nonlinear dynamics of human posture on rigid and compliant surfaces

The study of bipedal posture on rigid and compliant surfaces is of broad interest to neuroscience, cognition, and biomechanics. On one hand changes in the neuromuscular system due to disease or old age can lead to characteristic postural fluctuations and on the other hand training individuals on rigid and moving surfaces can improve balance and reduce the propensity to fall which is a major determinant in quality of life for aging populations. This thesis focuses on how ideas from nonlinear dynamics of reduced order dynamical systems can lead to better methods for analyzing experimental postural data to help explain postural behavior in a number of settings. First, an overview of the importance of studying postural dynamics is presented, followed by a literature review of the prior signal analysis and modeling works performed. Next, a signal analysis method using wavelet transforms to resolve postural fluctuation data about a stable equilibrium into several timescale components is discussed. Following this, the bifurcations of the upright equilibrium on a rigid surface are investigated using a simple inverted pendulum model. In addition, the presence of limit cycle behavior occurring in experimental postural data from subjects with a neuromuscular disorder are investigated. After this, the nonlinear dynamics and bifurcations of posture on a compliant surface are studied by coupling the previous model to a single degree-of-freedom balance board. The analysis of posture of a person standing on a balance board is extended to understand how a time delayed feedback on the balance board will alter stability the stability of posture. The thesis concludes with a summary of the key findings of this work and possible future directions