Dynamics of interaction network models: Linking dynamics to network structure
Interaction networks arise in many settings, including population models and chemical reactions. The underlying network (graph) consists of relevant biochemical reactions, and many mechanistic models are built in this manner. These models are flexible enough to allow for interesting dynamics, such as bistability and oscillations. Relating the model's dynamics to its network structure is both scientifically and mathematically important. On one hand, the subnetwork linked to the dynamics points to crucial processes for biological function. On the other hand, we can deduce certain qualitative dynamics from network motifs. This is possible because the dynamics can be attributed to said motifs. In this talk, I will introduce a graph based on the Jacobian matrix, and provide conditions from which one can infer/preclude asymptotic stability, bistability, and oscillations.
Bio: Dr. Yu received her PhD from the University of Wisconsin in 2021 and is currently and Independent Postdoctoral Fellow at the NSF-Simons Center for Mathematical and Statistical Analysis of Biology at Harvard University.
For those that will be unable to attend the talk in person, a Zoom link for this talk is also available: https://illinois.zoom.us/j/84076898467?pwd=NWVSZVBac0dGdHB1aHlDT3NBejJEUT09
