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

Abstract: 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 attractive (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. This is joint work with Gheorghe Craciun and Polly Yu.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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Seminar on the Mathematics of Reaction Networks

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This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom! Many of the talks are recorded; to see the recording, from Past Talks, open details of the listed talk for a video link.

The organizers.

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