Recognition of Phase Patterns in a Chemical Reactor Network

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Abstract

Phase shifts between four Belousov−Zhabotinsky (BZ) oscillators are applied to encode phase patterns in an experimental network consisting of four reactors. Oscillations are established in a focus of the BZ reaction, which is sinusoidally driven by an applied electrical current. In addition to the global electrical coupling by the sinusoidal function the four reactors are electrically coupled by an optimized feedback function including time delay. Two of three possible phase patterns can be encoded in this Hopfield-type network of four reactors. With a phase pattern in which all four reactors are in-phase, one of the two stored phase patterns is recalled with a 50% probability. This indicates that the two encoded patterns have the same dynamic stability. It is possible to reversibly switch between the two patterns by adding Ce4+ solution. Higher order phase patterns permit a higher phase resolution. The phase method provides for a large amount of information to be stored and recalled in a multiunit network. Numerical calculations with the seven-variable Györgyi−Field model of the BZ reaction are in good agreement with the experimental results. Generic similarities with the so-called binding problem in neurology are discussed.

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