Partial Differential Equations as Models for Social and Ecological Complex Systems
Location
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.