Before revision:  We then apply these technique to a class of single input, single output metabolic cycles, and find that stability is guaranteed under a wide range of conditions . Next, we extend our analysis to a small autocatalytic cycle, and determine parameter regimes within which the cycle is very likely to be stable.
After revision:  We then apply these techniques to a class of single input, single output metabolic cycles, and find that stability is guaranteed under a wide range of conditions . Next, we extend our analysis to a small autocatalytic cycle, and determine parameter regimes within which the cycle is very likely to be stable.