Chemical reaction networks: deterministic and stochastic models – Daniele Cappelletti (University of Wisconsin – Madison)

Venue

Sala Seminari (Dip. Matematica).

Abstract

Chemical reaction networks are mathematical models used in biochemistry, as well as in other fields. Specifically, the time evolution of a system of biochemical reactions are modelled either deterministically, by means of a system of ordinary differential equations, or stochastically, by means of a continuous time Markov chain. It is natural to wonder whether the dynamics of the two modelling regimes are linked, and whether properties of one model can shed light on the behavior of the other one. In this talk some connections will be shown, and both classical and recent results will be discussed. However, many open questions remain. For example, it is not known under what assumptions some qualitative properties of the deterministic model imply positive recurrence, non-explosiveness or absorption events for the stochastic model.

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