Doctor of Philosophy, Case Western Reserve University, 2024, Applied Mathematics
Physiological systems underlying vital behaviors, such as breathing, walking, and feeding, are controlled by closed-loop systems integrating central neural circuitry, biomechanics, and sensory feedback. The brain and body orchestration allows these motor systems to demonstrate crucial biological phenomena such as homeostasis, adaptability, and robustness. In this thesis, we investigate the role of sensory feedback in motor dynamics and control, based on an abstract model for motor pattern generation that combines central pattern generator (CPG) dynamics with a sensory feedback mechanism. Given the underdevelopment of control theory for limit cycle systems, we extend recently developed variational tools, which allow us to characterize the sensitivity of the systems to perturbations and changing conditions both within and outside the body. As concrete examples, we apply our methods to several closed-loop models with sensory feedback in place, including locomotion, ingestion, and respiration. Our analytic framework provides a mathematically grounded numerical quantification of the effects of a sustained perturbation on the rhythm performance and robustness, which is also broad enough to study control of oscillations in any nonlinear dynamical systems. Moreover, the observations we obtain from the examples provide important information for future work modeling neuro-motor rhythm generation and insights that have the potential to inform the design of control or rehabilitation systems.
Committee: Peter Thomas (Advisor); David Gurarie (Committee Member); Erkki Somersalo (Committee Member); Hillel Chiel (Committee Member)
Subjects: Applied Mathematics; Behavioral Sciences; Biology; Engineering; Mathematics; Neurosciences; Physiology