SIAM Conference on Applications of Dynamical Systems (DS25)

Since the dawn of stochastic chemical reaction network theory over 50 years ago, there have been many general results about (positive) recurrence, especially in the case of mass-action kinetics. One less-explored area is that of mass-action models whose rate constants, rather than being static, are themselves stochastic. Such models have relevance in applications, since biomolecular systems rarely exist in isolation and their rates often depend on time-changing quantities. In this series of two talks, we investigate the positive recurrence of one of the simplest cases of these stochastic rate constants models, with two species, at most monomolecular source complexes, and rate-constants that switch stochastically between two possible sets of options. Already in this special case, it will turn out that the possible overall behaviors are rich.

Specifically, in this talk I will introduce the topic and discuss when positive recurrence is achieved in two related settings: the first setting concerns networks with monomolecular complexes whose rates change stochastically over time, based on joint work with Abhishek Pal Majumder and Carsten Wiuf. The second setting concerns models with monomolecular source complexes (but general product complex) and rates randomly switching between two value sets at a low speed, based on joint work with Chuang Xu.

Sheraton Denver Downtown Hotel

Denver, CO, USA