Unveiling Surprising Connections Between the Classical Theory of Reaction Networks and Generalized Lotka-Volterra Systems

2023. 11. 21. 17:15
Diego Rojas La Luz (Wisconsin)

Joined work with Polly Yu (Harvard) and Gheorghe Craciun (Wisconsin)

We explore the relationship between Reaction Networks and Population Dynamics, with a specific focus on Generalized Lotka-Volterra systems. Surprisingly, we find strong analogies between classical Mass Action Kinetics results (like the Horn-Jackson theorem and the deficiency-zero theorem) and new counterparts in Generalized Lotka-Volterra systems, hinting at a deep connection, where previously none was known. Notably, in the Generalized Lotka-Volterra setting, we can prove that “complex-balanced” equilibria (properly defined) are globally attracting (which corresponds to the “global attractor conjecture" in the Reaction Networks setting). As an example, we show how to apply this new theory to characterize global stability for a large class of cooperative Generalized Lotka-Volterra systems. We can also extend our results to analyze the properties of variable-k systems, an area not fully explored in the context of Generalized Lotka-Volterra systems. This exploration unlocks untapped insights into the mathematical foundations of these systems, shedding light on their connections and paving the way for new avenues of research and discovery in this field.

Zoom link is available from the organizer of the seminar. Please contact János Tóth at jtoth(at)math.bme.hu.