Assessing a Kinetic System’s Vulnerability to Bifurcation-Induced Regime Shifts through Elementary Flux Mode Analysis

A regime shift occurs when small external variations in system parameters shift the system’s state from a nominal to an alternative qualitative behavior. This paper uses robust stability margins to evaluate a kinetic system’s vulnerability to bifurcation-induced regime shifts. The results are derived for an important class of nonnegative polynomial systems defined with respect to a directed graph characterizing mass/energy flows within the system. Such systems are sometimes called kinetic systems and they are often found in mathematical ecology and biochemical reaction networks. This paper characterizes a kinetic system’s robust stability in terms of the system’s elementary flux modes (EFM). EFM’s are often used to characterize fundamental pathways controlling an ecological or biochemical system’s function. We establish sufficient conditions characterizing the largest variation in EFM activity for which system’s equilibrium is guaranteed to be asymptotically stable with respect to a specified region of attraction. The main contribution is that these stability conditions can be posed as a separable bilinear program whose local solution can be obtained using quadratic programming software. These stability margins are used to evaluate the vulnerability to regime shifts for biochemical and ecological system exhibiting limit cycle behavior