**UoP maths seminar (2013-14)**

**Convergence to equilibria in order-preserving systems with an increasing linear first integral.**

*Speaker*: Pete Donnell

*Venue*: Wednesday 29th January 2014, 2pm, LG2.04a (refreshments provided)

*Abstract*: In systems of chemical reactions we might often expect simple behaviour such as global convergence to equilibria on physical grounds. This is backed up by numerical experiments on models constructed under a variety of different assumptions. However, it is generally hard to prove that such behaviour must occur for all initial conditions and all reasonable choices of reaction rates. In this talk, I will discuss an approach to proving global convergence to equilibria in certain classes of dynamical systems via nonexpansivity with respect to a polyhedral norm. Identifying a suitable norm for a given system is nontrivial, but it can be shown that monotone systems with an increasing linear first integral are nonexpansive with respect to non-standard norms. This theory can be applied to certain families of chemical reaction systems, showing that they exhibit global convergence to equilibria under weak assumptions on reaction rates.