Chemical reaction networks: deterministic and stochastic models

Tuesday, July 4, 2017
Ora Inizio: 
Ora Fine: 
Daniele Cappelletti
University of Wisconsin - Madison

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.