Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

An important feature of locomotion in cats, rats, and humans is that changes in speed occur due to a shortening of the stance (extensor) phase, while the swing (flexor) phase duration remains relatively constant. We have analyzed a simplified locomotor model that can replicate this key feature through feedback control. In this model, a central pattern generator (CPG) establishes a rhythm and controls the activity of a pendular limb, with afferent feedback signals closing the loop. Using dynamical systems methods, we analyze the mechanisms responsible for rhythm generation in the CPG, both in the presence and absence of feedback. We exploit our observations to construct a reduced model that is qualitatively similar to the original but tractable for rigorous discussion. We prove the existence of a locomotor cycle in this reduced system using a novel version of the Melnikov function, adapted for discontinuous systems. Finally we utilize our understanding of the model dynamics to explain its performance under various modifications, including recovery of oscillatory behavior after spinal cord injury and response to changes in load.