Recognition of Phase Patterns in a Chemical Reactor Network

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 Ce 4+ 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.

Biomolecular nonlinear dynamic mechanisms as a foundation for human traits of information processing machine

“…There were a number of experimental investigations and theoretical estimations that open the practical approaches to designing these systems (see Epstein, 1990;Laplante and Erneux, 1992;Hjelmfelt et al, 1993;Hjelmfelt and Ross, 1994;Laplante et al, 1995;Dechert et al, 1996).…”

Weak Chimeras in Modular Electrochemical Oscillator Networks

“…Different types of interactions were able to induce different synchronization patterns, e.g., in-phase, anti-phase, and out-of-phase entrainment. The CSTR technology however is difficult to scale up to a large population of reactors [7,8]. Belousov-Zhabotinsky (BZ) microdroplets [9,10], beads [11,12], microwell arrays [13], and nanodroplets [14] provide ways to study synchronization of populations.…”

Oregonator generalization as a minimal model of quorum sensing in Belousov–Zhabotinsky reaction with catalyst confinement in large populations of particles

“…20 These efforts yielded a variety of phenomena, including rhythm splitting, 1,3 phase-difference locking, 2,8-10,14-17 oscillator death 4,8,17,19,20 and rhythmogenesis, 5,19,20 entrained responses to pulsed forcing, 6,7,11,16 presynchronization, 14 quasiperiodicity, bursting and chaos, [10][11][12][13]15,17 or coupled chaotic states. 12,13 Moreover, investigations were also extended to three [21][22][23][24][25][26] or more interacting reactors, [27][28][29][30][31][32] offering further new insights into how these systems react to external stimuli in terms of their propagation 21,22,[27][28][29][30] or even information encoding and decoding. 31,32 Several approaches exist for studying the collective dynamics of even larger numbers of oscillators.…”

“…12,13 Moreover, investigations were also extended to three [21][22][23][24][25][26] or more interacting reactors, [27][28][29][30][31][32] offering further new insights into how these systems react to external stimuli in terms of their propagation 21,22,[27][28][29][30] or even information encoding and decoding. 31,32 Several approaches exist for studying the collective dynamics of even larger numbers of oscillators. A remarkable body of experimental evidence has been collected for arrays of globally coupled electrodes 33 that can exhibit chaotic synchronization, [34][35][36][37][38] Kuramoto phase synchronization, [39][40][41][42][43] noise coherence, [44][45][46] amplitude death, 47 resonant clusters, 48 desynchronization, 49 effects of non-isochronicity, 50,51 and even genuine chimera symmetry breaking.…”