(600bu) Systematic Analysis and Prediction of Steady State Multiplicity Patterns

Autocatalytic reactions and processes are commonly encountered in growth of all living cells, processes involving free radicals, polymerization processes, many inorganic and organic reactions, and crystallization processes. A comprehensive analysis of steady state multiplicity of single and two parallel autocatalytic reactions occurring in a well-mixed reactor is presented. The generation of the autocatalyst from competing resources is followed by its decay. Parallel autocatalysis is observed in growth of living cells on multiple substitutable resources (nutrients) and co-metabolism of primary and secondary nutrients (simultaneous utilization of multiple nutrients via independent metabolic pathways inside living cells). A single well-mixed reactor may operate at up to five steady states.  The space of ratios of the kinetic parameters for the autocatalytic reactions and ratios of supply of resources is divided into different regions depending on the maximum number of steady states admissible, which vary from three to five. The space of the remaining kinetic and operating parameters is divided into multiple regions based on the number of physically realizable steady states. This division allows exact determination of appearance and disappearance of particular steady states. Continuation curves for limit point bifurcation are identified in the multi-dimensional kinetic and operating parameter space. The reaction system exhibits a rich variety of steady state patterns. Steady state multiplicity patterns, such as isolas and mushrooms, are predicted in a non-iterative fashion by a judicious choice of parameter combinations. In prior studies, these have been obtained via extensive iterations involving sweeps through parameter spaces. The present approach enables easier identification of multitude of rich multiplicity patterns.