Advisor: Leah Shaw
Description: Many complex systems can be modeled as a network. There has recently been a lot of interest in adaptive networks, where the nodes and connections between them change over time. Current methods for analyzing adaptive networks can handle discrete node states (nodes can take on a few discrete values such as susceptible or infected in a disease model) and binary links (nodes are either connected or disconnected). However, systems like neural networks in the brain or opinion dynamics in a social network could be better modeled if states and connections were continuous variables. We would like to extend analytic methods to handle these cases by generalizing them from ordinary differential equations to partial differential equations. The project will also involve simulating adaptive networks to test our methods.
Courses: 302 strongly preferred, otherwise 345 or other prior exposure to differential equations needed, 441 or 442 nice but not necessary