Abstract: 

The Lotka–Volterra system is the following second-order autonomous system of differential equations: \begin{align*} \begin{dcases} x'=ax^2+bxy\\ y'=cxy+dy^2. \end{dcases} \end{align*} The solution sets of the systems can be viewed as definable sets in the theory of differentially closed fields of characteristic zero. In this talk, I will discuss approaches to determining their model-theoretic properties, including strong minimality, geometric triviality, and strict disintegratedness. Combining these properties with concrete translations of model theory in ordinary differential equation, we establish algebraic independence results for solutions within a single Lotka–Volterra system and across different systems.