Stability analysis of a class of biological network models

In this paper, we establish stability conditions for a special class of interconnected systems arisen in several biochemical applications. It is known that most of the biochemical processes can be represented using quasi-polynomial systems. We show that a special class of quasi-polynomial systems can be cast in the Lotka-Volterra canonical form. We study the asymptotic stability properties of a class of quasi-polynomial systems which are relevant to biological network models. First, we show that under some sufficient conditions the solutions of the quasi-polynomial systems (in the positive orthant) converge to the set of equilibrium points. These results are applied to parameterized models of three different biological systems: generalized mass action (GMA) model, an oscillating biochemical network, and a reduced order model with Hill function. We show that one can find the range of parameters for which a given parameterized model is stable.