Nonlinear analyses of periodic and chaotic time series from the peroxidase-oxidase reaction

Experimental time series of [O₂] generated by the peroxidase-oxidase reaction were analyzed using various methods from nonlinear dynamics. The following results were obtained: (1) Aperiodic time series are chaotic as evidenced by (i) the observation of period doubling bifurcations in response to increasing the amount of 2,4-dichlorophenol in the reaction mixture, (ii) well-defined next amplitude maps, (iii) positive Lyapunov exponents corresponding to about 0.5 bits per orbital excursion, and (iv) fractal dimensions ranging from 2.6 to 2.8. Prediction profiles obtained by subjecting the data to nonlinear forecasting give further evidence of deterministic chaos. (2) The chaotic data are nonuniform, since none of the above-mentioned methods work well when applied to the continuous data. Instead, one has to use a series of maxima. (3) Conclusions 1 and 2 are supported by the fact that similar results obtain for chaotic time series generated by a simple model of the reaction.