Statics and dynamics of multiple cubic autocatalytic reactions

Static and dynamic properties of multiple cubic autocatalytic reactions in an isothermal continuous stirred tank reactor are investigated. It is shown that in the bifurcation diagram of the system should an n-interaction isola exist, it is to reside in the intersection of all possible (n−1)-interaction isolas of the n species constituting the n-interaction. Next, it is discussed that once the ratio of reproduction to death rates for a species is fixed, then the size of its single species isola is fixed, in logarithmic residence time. Furthermore, it is found that any interaction isola in the bifurcation diagram is unstable, whereas single species isolas will have ranges of stable steady states. Finally, these findings and some dynamic properties of the system are demonstrated in case studies.