Event Series
Event Type
Seminar
Wednesday, May 12, 2021 12:00 PM
Nancy Rodriguez (University of Colorado)

The use of PDEs to model social and ecological complex systems has been popularized in the past decades.  In this talk, I will present two recent works in this area. In the first part of the talk, I present a unifying model for the dynamics of ecological populations and street vendors, an important part of many informal economies.  

I discuss the effects of directed movement of populations subject to the Allee Effect.  Particularly, we will discuss whether directed movement can help a population overcome the Allee effect.  I will conclude this section by making a connection to the Ideal Free Distribution and analyze what happens under competition, showing that an Ideal Free Distribution strategy is a local neighborhood invader strategy.  The second part of the talk will focus on a model for urban crime with police dynamics.  We discuss the richness of the solution behavior depending on the parameters, including spatially heterogeneous solutions, time-periodic solutions, and an ill-posed parameter regime.