Before revision:  The guaranteed stability of a class of single input, single output metabolic cycles is established . Next, parameter regimes for the stability of a small autocatalytic cycle are determined. It is demonstrated that analytical methods can be used to understand the relationship between kinetic parameters and stability, and that results from these analytical methods can be confirmed with computational experiments.
After revision:  The guaranteed stability of a class of single input, single output metabolic cycles is established . Next, parameter regimes for the stability of a small autocatalytic cycle , and determine parameter regimes within which the cycle is very likely to be stable. We demonstrate that analytical methods can be used to understand the relationship between kinetic parameters and stability, and that results from these analytical methods can be confirmed with computational experiments.