Using Distance to Bifurcation to Quantify the Resilience of Nonnegative Dynamical Systems

This paper describes the use of sums-of-square (SOS) program to compute a resilience measure for nonnegative dynamical systems. Such measure is defined as the distance between system’s nominal parameter and the closest critical paramater at which a bifurcation occur. Our proposed method uses a modeling formalism from chemical reaction network theory to describe the dynamics of nonnegative system. We show that such modeling formalism allow us to describe the bifurcation condition only in term of system’s parameter. The SOS program for computing the distance to the closest bifurcation is formulated using the positvstellensatz concept from real algebraic geometry and the SOS relaxation technique in semidefinite programming.