Dynamical Activation in Autocatalytic Chemical Networks: A Correlation Dimension Analysis

Dynamical Activation in Autocatalytic Chemical Networks: A Correlation Dimension Analysis (v2 — corrected kinetics) We investigate the relationship between autocatalysis and dynamical complexity in chemical reaction networks using correlation dimension analysis. Defining an activation ratio η = D₂/r_S that compares the attractor dimension D₂ to the stoichiometric degrees of freedom r_S, we test whether additional autocatalytic reactions increase dynamical activation. Using the Brusselator oscillator as a template with chemostatted food species, we find that randomly added reactions tend to increase r_S faster than they increase D₂, leading to a net decrease in η. Control (non-autocatalytic) and test (autocatalytic) additions produce indistinguishable η distributions, indicating that the dilution effect is driven by stoichiometric expansion rather than the autocatalytic character of the additions. These results demonstrate that dynamical activation depends critically on network topology rather than the quantity of autocatalytic reactions, and that the distinction between structural possibility and dynamical realization is essential for understanding chemical complexity. v2 correction note: The original version contained a bug in the reaction rate parser affecting repeated-species reactant stoichiometry (e.g., X + X + Y → 3X was computed as k·X·Y instead of k·X²·Y). All results have been recomputed with corrected kinetics and chemostat boundary conditions. The qualitative conclusion that randomly added reactions dilute η is confirmed under corrected kinetics. The v1 finding of increased η variance for autocatalytic additions is not reproduced; both groups show identical η distributions.