No abstract

No abstract

No abstract

We present a chemical realization of the Boolean functions AND, OR, NAND, and NOR with a neutralization reaction carried out in three coupled continuous flow stirred tank reactors (CSTR). Two of these CSTR's are used as input reactors, the third reactor marks the output. The chemical reaction is the neutralization of hydrochloric acid (HCl) with sodium hydroxide (NaOH) in the presence of phenolphtalein as an indicator, which is red in alkaline solutions and colorless in acidic solutions representing the two binary states 1 and 0, respectively. The time required for a "chemical computation" is determined by the flow rate of reactant solutions into the reactors since the neutralization reaction itself is very fast. While the acid flow to all reactors is equal and constant, the flow rate of NaOH solution controls the states of the input reactors. The connectivities between the input and output reactors determine the flow rate of NaOH solution into the output reactor, according to the chosen Boolean function. Thus the state of the output reactor depends on the states of the input reactors.

Deterministic chaos in the Belousov-Zhabotinsky reaction is well-known to occur at low flow rates.Id However, the source of aperiodicity in the high flow rate region has remained a controversial issue. We reproduced the aperiodicity found by Hudson7v8 and, more recently, by Noszticzius et al.9 under practically identical experimental conditions. We interpret the observed aperiodicity at high flow rates as nonchaotic on the basis of the 1-D maps and Renyi dimensions (calculated with the nearest neighbor method' from single value decomposition reconstructed'O attractors), including the Hausdorff dimension.The observed aperiodicity at high flow rates is most probably a noisy time series of the 1 ' l 2 state and the adjoining Farey ordered states.