Computational topology is an emerging mathematical tool that is well-suited to numerical studies of dynamical systems. I will describe two projects that use computational topology to measure dynamics. The first measures density patterns in a coupled-patch population model and seeks to detect early warning signals of regime shifts. The second detects and builds a symbolic model for complicated dynamics in a continuous space (integrodifference) population model. Time permitting, I will discuss future plans for these techniques and the implications for avoiding explicit model construction in the study of some physical systems.
Population Dynamics via Computational Topology
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