Dear Colleagues,

We are pleased to invite you to the following SPASS seminar (jointly organised by UniPi, SNS, UniFi and UniSi):

Speaker: Lucie Laurence (University of Bern, Institute of Mathematical Statistics and Actuarial Sciences)

Title: Noise-induced stabilization in chemical reaction networks

Date and time: Tue, May 5th at 14:00 CET

Place: Auletta Riunioni, Dipartimento di Matematica, UniPi, Pisa

Join online: https://meet.google.com/esx-pxkw-fhw

On behalf of the organisers,
Samuele Saviozzi

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Abstract:

Chemical reaction networks (CRNs) describe the evolution of interacting molecular species through a set of reactions. In the stochastic formulation, the system tracks discrete molecule counts and evolves as a jump process driven by reaction events. Transition rates follow mass‑action kinetics and are polynomial functions of the state. When molecule numbers are large, these stochastic dynamics are typically approximated by a deterministic ODE system. The connection between the stability of these two models is an active area of research.

In this talk, I will present a CRN exhibiting a noise‑induced stabilization phenomenon. Deterministically, the associated ODE admits trajectories that diverge and blow up in finite time. In contrast, the stochastic model is stable: sample paths remain bounded and repeatedly return to compact regions of the state space. The proof combines a Lyapunov‑function criterion with scaling arguments that control the behavior of the stochastic trajectories.

In the final part of the talk, I will discuss new directions for extending this stabilization result to broader classes of CRNs. Using Poincaré compactification, I will outline conditions on the deterministic dynamics that ensure stability of the corresponding stochastic system.

This is a joint work with A. Agazzi.