SIAM Conference on Applied Algebraic Geometry (AG19)

Stochastic reaction networks are mathematical models heavily utilized to describe the time evolution of biological systems, when few active molecules are present. In this case, the system dynamics is stochastic, and the changes of the molecules counts are described by means of a continuous time Markov chain.

Despite the large use of these models, simple questions concerning the existence of a stationary distribution are hard to answer to, except for few exception, and constitute an active area of research. Often, in order to prove the convergence of a model to a stationary distribution, a suitable Lyapunov function is sought. The typical problem with this approach is that the drift of the usual candidate functions fail to be negative along the state space borders. I will present a novel and fast convex programming technique to check for the existence of a piecewise linear Lyapunov function. Such technique utilizes the geometry of the network and divides the state space in different regions to overcome the typical border problems which arise when looking for suitable Lyapunov functions.

University of Bern, Bern, Switzerland

Bern, Switzerland