Investigating the effects of network structure and afferent feedback in models of rhythmic movement

Animals can generate distinct rhythmic behaviors using a shared set of muscles and motoneurons, and in certain cases, the structure responsible for generating these movements is unknown. Distinct networks could be dedicated solely to particular behaviors, a singular network could control various movements through reorganization or under different inputs, or a hybrid of these two concepts could exist. In the first chapter of this thesis, we explore the compatibility of different network characteristics with experimental results regarding swimming and scratching rhythm generation in the turtle. We propose three distinct architectures that represent a range of connectivity between networks responsible for these rhythms, and test their performance against a set of experimental benchmarks regarding dual stimulation. The results of our modeling concur with experimental results, suggesting that networks that generate locomotion and scratching share important components.\ud \ud In the second and third chapters, we focus our attention on a previously published neuromechanical locomotor model. In this closed loop system, a central pattern generator (CPG) establishes a rhythm under sufficient supra-spinal drive and controls the activity of a pendular limb, which sends afferent signals back to the CPG, affecting its operation. Increasing the drive to the CPG increases the limb frequency through changes in the stance phase duration only, which is a key feature of normal overground locomotion.\ud Using geometric singular perturbation theory, 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. We highlight how the limb dynamics shape overall model behavior, and indicate a crucial relationship between components\ud that controls the model's asymmetric response to drive changes. 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