Algebraic relations between solutions of Lotka-Volterra systems: a complete classification.
Abstract: The classical Lotka-Volterra (LV) systems are used in population dynamics to provide a very simplified model of predator-prey interactions. It is natural to ask if there are any relations between solutions of these systems for different initial values and/or different parameters. As one of the simplest systems of non-linear algebraic differential equations, the LV systems are a good test case for recently developed model-theoretic methods to answer these questions. In this talk, I will provide a complete classification of algebraic relations between solutions of LV systems, and explain how model theory plays a key role in this endeavor. This is joint work with Yutong Duan and Christine Eagles, with some important input from work of Duan and Ronnie Nagloo.