Pulses in heterogeneous media
Complex systems arise when many simple identical, or nonidentical, units are coupled together. For example, living tissues are comprised of very large numbers of individual cells, and entire organs perform functions that are not possible at the cellular level. Mathematical physiology has led to a myriad of models of individual cell function, often focussing on the dynamics of transport of ions and more complicated molecules within and between cells. Many such models exhibit excitability, wherein a small external stimulus leads to a large response before a return to steady state. When a network of these subsystems is coupled together, pulses can travel through the network, stimulating an excited response in subsystems that are unable to respond that way in isolation. This project will apply a variety of classical and new dynamical systems techniques to understand this situation, including investigating what insights are provided by Koopman modes computed via dynamic mode decomposition.
Supervisor: Rua Murray
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