Measuring Complexity in Reactor Networks with Cubic Autocatalytic Reactions

Systems with high steady-state multiplicity and rich dynamic behavior are difficult to investigate using conventional reductionist methods. A network of more than five reactors hosting cubic autocatalytic reactions may potentially have more than 10^2 steady states and many distinct dynamic regimes, all for the same parameter set. This paper discusses how the static complexity of such systems can be measured to give a holistic picture. To achieve this, stochastic simulations were performed to statistically determine the bifurcation structure of the system, and the gathered information is summarized using a measure akin to fractal dimension. With this measure, the growth of static complexity is investigated as a function of the network size.