Cellular systems—I. stability of chemical systems

Abstract

In this work, we attempt to formulate and partially resolve the “complexity vs. stability” problem in open chemical systems, in the framework of Lyapunov's second method. Sufficient conditions are given for stability of the steady state of a chemical system under structural perturbations caused by interactions among the chemical species in the system. As a byproduct of this analysis, we will show important properties of the self-inhibitory chemical systems, and establish the tolerance of the stability to a broad class of perturbations. Finally, biological open systems are exhibited in order to show the scope of our stability analysis.